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ON THE RESTRICTED BURNSIDE PROBLEM [chapter]

EFIM I. ZELMANOV
<span title="">1997</span> <i title="CO-PUBLISHED WITH SINGAPORE UNIVERSITY PRESS"> World Scientific Series in 20th Century Mathematics </i> &nbsp;
This theorem has some applications to the General Burnside Problem in group varieties and to compact groups.  ...  To appreciate the impact this problem had on the Ring Theory let us mention that N. Jacobson's Structure Theory of Algebras was stimulated by the Kurosh Problem and I.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/9789812385215_0067">doi:10.1142/9789812385215_0067</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bphrxy453bhejkwo3kofgokheu">fatcat:bphrxy453bhejkwo3kofgokheu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170811094932/http://www.mathunion.org/ICM/ICM1990.1/Main/icm1990.1.0395.0402.ocr.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/61/09/6109c6f354fdcfbff1dfe6a973eb49476f4eef52.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/9789812385215_0067"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Page 6182 of Mathematical Reviews Vol. , Issue 98J [page]

<span title="">1998</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The author’s objective is to study Golod’s examples, to generalize them and to demonstrate their usefulness for the so- lution of numerous problems other than those of Burnside and Kurosh.  ...  For many years, both the Burnside problem and the Kurosh prob- lem were believed to have a positive answer, mainly because this was the case in numerous special situations.  ... 
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SOME OPEN PROBLEMS IN THE THEORY OF INFINITE DIMENSIONAL ALGEBRAS

Efim Zelmanov
<span title="2007-09-30">2007</span> <i title="The Korean Mathematical Society"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/i62hw3svkbajvonwzemy75kjmq" style="color: black;">Journal of the Korean Mathematical Society</a> </i> &nbsp;
We will discuss some very old and some new open problems concerning infinite dimensional algebras. All these problems have been inspired by combinatorial group theory.  ...  The Burnside and Kurosh problems In 1902 W.  ...  Kurosh [24] (and independently J.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4134/jkms.2007.44.5.1185">doi:10.4134/jkms.2007.44.5.1185</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7rzyi5baknbjdmlumeqbaliiyi">fatcat:7rzyi5baknbjdmlumeqbaliiyi</a> </span>
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On Kurosh problem in varieties of algebras [article]

Dmitri Piontkovski
<span title="2009-05-28">2009</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Our approach is the following: we translate the problem to the language of operads and then apply usual homological constructions, in order to adopt Golod's solution of the original Kurosh problem.  ...  We consider a couple of versions of classical Kurosh problem (whether there is an infinite-dimensional algebraic algebra?) for varieties of linear multioperator algebras over a field.  ...  The next claim gives a stronger version of Kurosh problem, that is, the Burnside problem. Corollary 4.4 (Burnside problem for multi-operational algebras).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0905.4748v1">arXiv:0905.4748v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hy7nz7vb4benxh3hrc6njuj4hi">fatcat:hy7nz7vb4benxh3hrc6njuj4hi</a> </span>
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On the Kurosh problem in varieties of algebras

D. I. Piontkovski
<span title="2009-11-18">2009</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uthuanwbp5dnbly3kjw3ltqx4a" style="color: black;">Journal of Mathematical Sciences</a> </i> &nbsp;
Our approach is the following: we cast the problem in the language of operads and then apply the usual homological constructions in order to adopt Golod's solution to the original Kurosh problem.  ...  We consider a couple of versions of the classical Kurosh problem (whether there is an infinite-dimensional algebraic algebra) for varieties of linear multioperator algebras over a field.  ...  The next claim gives a stronger version of the Kurosh problem, i.e., the Burnside problem. Corollary 4.4 (the Burnside problem for multi-operational algebras).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10958-009-9711-9">doi:10.1007/s10958-009-9711-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qrgxmf2zprcovo6d2dltl6bf2a">fatcat:qrgxmf2zprcovo6d2dltl6bf2a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190226141420/http://pdfs.semanticscholar.org/725f/8d8106c101986eec48e43e5ecfcdb50a14ac.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/72/5f/725f8d8106c101986eec48e43e5ecfcdb50a14ac.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10958-009-9711-9"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Page 595 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 52, Issue 7 [page]

<span title="">1946</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_american-mathematical-society-bulletin" style="color: black;">American Mathematical Society. Bulletin of the American Mathematical Society </a> </i> &nbsp;
Irving Kaplansky: On a problem of Kurosh and Jacobson. (Ab- stract 52-5-122.) 11. Grace E. Bates: Free loops and nets and their generalizations. (Abstract 52-5-105.) 12.  ...  Jones: Semimodular finite groups and the Burnside basis theorem. (Abstract 52-5-120.) 14. F. B. Jones: A characterization of a plane semi-locally-connected continuum. (Abstract 52-3-101.) 15.  ... 
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Page 1277 of Mathematical Reviews Vol. , Issue 94c [page]

<span title="">1994</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Burnside problem.  ...  In the first chapter we consider the Kurosh-Levitzki problem in associative algebras. The second chapter is devoted to the Kurosh-Levitzki problem in Jordan al- gebras.  ... 
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Book Review: Noncommutative rings

Maria J. Wonenburger
<span title="1969-07-01">1969</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hjoli2j6qffdpaalkszryuidk4" style="color: black;">Bulletin of the American Mathematical Society</a> </i> &nbsp;
A short final chapter offers part of the recent work (1964) of Golod and Shafarevich and its applications in showing that the answer to the general Burnside and Kurosh problems is in the negative.  ...  Besides seeing the theory at work in the study of groups of matrices, group representations, and in settling the problems of Burnside and Kurosh, there are, or there are given the bases for the construction  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9904-1969-12256-1">doi:10.1090/s0002-9904-1969-12256-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/k6viddhfinhjxcj7tmb3i5z73m">fatcat:k6viddhfinhjxcj7tmb3i5z73m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160304064344/http://www.ams.org/journals/bull/1969-75-04/S0002-9904-1969-12256-1/S0002-9904-1969-12256-1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1f/11/1f11d7c192a4418e63fd54a4f6ccf63ddee0cd5c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9904-1969-12256-1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Page 251 of Mathematical Reviews Vol. 21, Issue 3 [page]

<span title="">1960</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The Burnside Problem for exponent n (not to be confused with several “restricted” Burnside Problems) is the question as to whether B(n, k) is finite for every positive k.  ...  Solution of the Burnside problem for exponent six. Illinois J. Math. 2 (1958), 764-786.  ... 
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Page 3254 of Mathematical Reviews Vol. , Issue 90F [page]

<span title="">1990</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Jean-Eric Pin (Paris) 90f:20097 20M10 16A38 Song, Guang Tian (PRC-LAN) The application of Lyndon words in the Kurosh problem for PI-algebras and in the Burnside problem for semigroups.  ...  (N.S.) 41(83) (1957), 381-394; MR 19, 727] about the Kurosh problem for PlI-algebras by using Lyn- don words and combinatorial methods. Using similar methods we improve a theorem of A. Restivo [J.  ... 
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Page 60 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 51, Issue 1 [page]

<span title="">1945</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_american-mathematical-society-bulletin" style="color: black;">American Mathematical Society. Bulletin of the American Mathematical Society </a> </i> &nbsp;
This is a special case of a problem recently proposed by Kurosh and it is analogous to the well known Burnside problem in the theory of groups.  ...  Nathan Jacobson: A problem on algebraic algebras.  ... 
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Page 450 of Mathematical Reviews Vol. 51, Issue 2 [page]

<span title="">1976</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
In Chapter 6 the Kurosh problem (are algebraic algebras locally finite?) and the Burnside problem (are torsion groups locally finite?)  ...  conjecture and a special case of the Burnside conjecture follow as corollaries.  ... 
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Page 3788 of Mathematical Reviews Vol. , Issue 99f [page]

<span title="">1999</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Among these problems are the problems of Burnside type (the Kurosh problem, the Shirshov height theorem, the nilpotency of the radical of finitely generated Pl-algebras), the growth of algebras and Gel  ...  of words to canonical form, the pumping-over procedure, the Kurosh problem and its relation with the Shirshov theorem), regular words in Lie algebras (including the theory of sandwiches and the specific  ... 
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Rational languages and the Burnside problem

Antonio Restivo, Christophe Reutenaeur
<span title="">1985</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
The problem of finding regularity conditions for languages is, via the syntactic monoid, closely related to the classical Burnside problem.  ...  This survey paper presents several results and conjectures in this direction as well as on related subjects, including bounded languages, pumping, square-free words, commutativity, and rational power series  ...  McNaughton and B. Rozoy for several comments, J. Beauquier, L. Boasson and M. Latteux for advices on context-free languages, P.E. Schupp for a history of the original Burnside problem, and J.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(85)90156-2">doi:10.1016/0304-3975(85)90156-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2n4rt47oebgypnh5ilw4iw5sme">fatcat:2n4rt47oebgypnh5ilw4iw5sme</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170921232118/http://www.lacim.uqam.ca/%7Echristo/Publi%C3%A9s/1985/Rational%20Burnside.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/96/3b/963bfd8e95183d37bcf102ab231dba5ac95a2e2e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(85)90156-2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Rational languages and the Burnside problem

A Restivo
<span title="">1985</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
The problem of finding regularity conditions for languages is, via the syntactic monoid, closely related to the classical Burnside problem.  ...  This survey paper presents several results and conjectures in this direction as well as on related subjects, including bounded languages, pumping, square-free words, commutativity, and rational power series  ...  McNaughton and B. Rozoy for several comments, J. Beauquier, L. Boasson and M. Latteux for advices on context-free languages, P.E. Schupp for a history of the original Burnside problem, and J.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(85)90104-5">doi:10.1016/0304-3975(85)90104-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ymjm5raelvad5ny7jqbo22uzsy">fatcat:ymjm5raelvad5ny7jqbo22uzsy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170921232118/http://www.lacim.uqam.ca/%7Echristo/Publi%C3%A9s/1985/Rational%20Burnside.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/96/3b/963bfd8e95183d37bcf102ab231dba5ac95a2e2e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(85)90104-5"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>
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