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2004 International journal of algebra and computation  
Then their free product G = G 1 * · · · * G m is 2-product subgroup separable in the pro-C topology of G.  ...  groups, then the product subset H 1 · · · H n is closed in the pro-C topology of R.  ... 
doi:10.1142/s0218196704001992 fatcat:6zwjprb3irahbbi3ui6rkfwklm

On the profinite topology of right-angled Artin groups [article]

V. Metaftsis, E. Raptis
2009 arXiv   pre-print
Moreover, we investigate the profinite topology of the direct product of two free groups.  ...  We show that the profinite topology of the above group is strongly connected with the profinite topology of the free group of rank two.  ...  Acknowledgement The first author would like to thank Armando Martino for various conversations concerning the profinite topology of F 2 × F 2 .  ... 
arXiv:math/0608190v4 fatcat:t7zdy4p7bbb6rbysx27rvmvuuq

Addendum to "Groups with the same cohomology as their profinite completions" [J. Algebra 320 (4) (2008) 1704–1722]

Karl Lorensen
2009 Journal of Algebra  
Acknowledgments I would like to thank the Erwin Schrödinger Institute for Mathematical Physics in Vienna, Austria for its invitation to participate in the Workshop on Profinite Groups in December 2008.  ...  It was at this conference that I became acquainted with much of the literature cited above.  ...  Much of Section 3 in the above paper revolves around three related issues: (1) quasipotency of groups; (2) the conditions under which the factors in a free product with amalgamation are topologically  ... 
doi:10.1016/j.jalgebra.2009.07.033 fatcat:i7l4lyqszjde5aswg53ewiqlea

On the profinite topology of right-angled Artin groups

V. Metaftsis, E. Raptis
2008 Journal of Algebra  
Moreover, we investigate the profinite topology of F 2 × F 2 and we show that the profinite topology of the above group is strongly connected with the profinite topology of F 2 .  ...  In the present work, we give necessary and sufficient conditions on the graph of a right-angled Artin group that determine whether the group is subgroup separable or not.  ...  Acknowledgments The first author would like to thank Armando Martino for various conversations concerning the profinite topology of F 2 × F 2 .  ... 
doi:10.1016/j.jalgebra.2008.03.031 fatcat:qdpqpn2we5euhdwopsjm5ei2nu

Page 7162 of Mathematical Reviews Vol. , Issue 2002J [page]

2002 Mathematical Reviews  
In particular, it is shown that the minimal ideal of the free profinite semigroup on a finite set with more than two generators is not a relatively free profinite completely simple semigroup.  ...  In this paper the authors define a profi- nite variety to be a class of profinite semigroups closed under arbitrary products and (profinite) divisors, then show that the lat- tice of such varieties is  ... 

Page 3338 of Mathematical Reviews Vol. 58, Issue 5 [page]

1979 Mathematical Reviews  
Special stress is laid on the theory of profinite groups on a topological space and on the theory of free products of profinite groups indexed by a topologi- cal space. ‘ The article consists of four chapters  ...  The structure of a free pro-C product I, G, of pro-C free groups on a topological space X is studied. Such a product is expressed as a projective limit of free products on finite spaces.  ... 

Page 2893 of Mathematical Reviews Vol. , Issue 97E [page]

1997 Mathematical Reviews  
If A is a profinite set and F denotes the free V-profinite semigroup on A, then the free U + V- profinite semigroup on A is a closed subsemigroup of a semidirect product of the free U-profinite semigroup  ...  The current paper provides an entirely analogous description of the free profinite semigroups, over profinite sets, in the pseudovariety semidirect product U « V of pseudovarieties U and V.  ... 

Subspace Topologies in Central Extensions

Martyn Quick
2001 Journal of Algebra  
As an application, it is shown that any finite abelian group can be embedded in the profinite completion of some countable torsion-free residually finite nilpotent group of class two and that of some finitely  ...  The possibilities for the topology induced on the centre by the profinite topology of nilpotent groups of class two and finitely generated centre-by-metabelian groups are examined.  ...  For example, Lubotzky [3] has shown that there exists a finitely generated torsion-free residually finite group whose profinite completion contains the Cartesian product of all finite groups.  ... 
doi:10.1006/jabr.2001.8915 fatcat:4s3w6xq2rvglzcic2q6xh65lia

On hereditarily just infinite profinite groups obtained via iterated wreath products [article]

Matteo Vannacci
2015 arXiv   pre-print
We study a generalisation of the family of non-(virtually pro-p) hereditarily just infinite profinite groups introduced by J. S. Wilson in 2010.  ...  We prove that this family contains groups of finite lower rank. We also show that many groups in this family are not topologically finitely presentable.  ...  I also wish to thank Eugenio Giannelli and Benjamin Klopsch for the most useful discussions, in particular I am grateful to the latter for the suggestion of Theorem 2.  ... 
arXiv:1506.00139v1 fatcat:buf5zputi5huxmyg4cuhgqyi44


Francesco G. Russo
2016 Bulletin of the Korean Mathematical Society  
The properties of the nonabelian tensor products are interesting in different contexts of algebraic topology and group theory.  ...  We prove two theorems, dealing with the nonabelian tensor products of projective limits of finite groups. The first describes their topology.  ...  Finally, the present researches are supported in part by NRF (South Africa) for the Grant No. 93652 and in part from the Launching Grant No. 459235 of the University of Cape Town (South Africa).  ... 
doi:10.4134/bkms.b150297 fatcat:uhln7ohpdzbmbfswsbxusozcrq


2007 International journal of algebra and computation  
A limit group is a finitely generated subgroup of a residually free group. We prove the result announced in the tittle.  ...  Note that if the profinite topology on G is efficient, then by the universal property for the profinite amalgamated free product, the profinite completion G of G is the profinite amalgamated free product  ...  in the profinite topology of G.  ... 
doi:10.1142/s0218196707003810 fatcat:c43sclwwwjas5ofygskx5csln4

Conjugacy Separability of Amalgamated Free Products of Groups

Luis Ribes, Pavel A. Zalesskii
1996 Journal of Algebra  
adopts the appropriate definition of a profinite fundamental group of a profinite graph of Ž w x. profinite groups cf. 27 . amalgamated free product.  ...  When 1 1 ⌫ s ⌫ *⌫is a profinite amalgamated free product, ⌫ can be similarly 1 ⌬ 2 interpreted as the profinite fundamental group of the graph of profinite groups over a graph consisting of one edge  ...  Let G and G be groups that are free-by-finite or finitely 1 2 Ž . generated nilpotent-by-finite not necessarily both of the same type , and assume that H is a common cyclic subgroup of G and G .  ... 
doi:10.1006/jabr.1996.0035 fatcat:al643cl6lrfqvewtmoninqsm74

Ascending HNN extensions of polycyclic groups have the same cohomology as their profinite completions [article]

Karl Lorensen
2010 arXiv   pre-print
Furthermore, let Ĝ∗̂_̂ϕ̂ be the profinite completion of G∗_ϕ.  ...  Assume G is a polycyclic group and ϕ:G→ G an endomorphism.  ...  In addition, he is indebted to Peter Symonds for enlightening him regarding profinite homology.  ... 
arXiv:1009.2645v5 fatcat:5bickx2ssfhnzcudknu7zjd6nq

Protori and Torsion-Free Abelian Groups [article]

Wayne Lewis
2019 arXiv   pre-print
A morphism between protori lifts to a product morphism between the universal covers, so morphisms in the category can be studied as pairs of maps: homomorphisms between finitely generated profinite abelian  ...  A finite rank torsion-free abelian group X is algebraically isomorphic to a canonical dense subgroup X_G of its Pontryagin dual G.  ...  Finitely generated in the context of profinite groups will always mean topologically finitely generated.  ... 
arXiv:1903.08022v1 fatcat:np7ietgsdzbqdewvuyxvtgnorq

Profinite extensions of centralizers and the profinite completion of limit groups [article]

Pavel Zalesskii, Theo Zapata
2017 arXiv   pre-print
groups (in the sense of Z.  ...  We introduce and investigate a class of profinite groups defined via extensions of centralizers analogous to the extensively studied class of finitely generated fully residually free groups, that is, limit  ...  By [RZ00b, Lemma 3.1.4(a) and Lemma 3.1.5(a)], the profinite topology of Γ n induces the profinite topology on Υ and the profinite topology of Υ induces the profinite topology on Γ.  ... 
arXiv:1711.01500v1 fatcat:r66bxijc6jftbh4cw7aalzex7a
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