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PROFINITE TOPOLOGIES IN FREE PRODUCTS OF GROUPS

2004
*
International journal of algebra and computation
*

Then their

doi:10.1142/s0218196704001992
fatcat:6zwjprb3irahbbi3ui6rkfwklm
*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. ...##
###
On the profinite topology of right-angled Artin groups
[article]

2009
*
arXiv
*
pre-print

Moreover, we investigate the

arXiv:math/0608190v4
fatcat:t7zdy4p7bbb6rbysx27rvmvuuq
*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 . ...##
###
Addendum to "Groups with the same cohomology as their profinite completions" [J. Algebra 320 (4) (2008) 1704–1722]

2009
*
Journal of Algebra
*

Acknowledgments I would like to thank the Erwin Schrödinger Institute for Mathematical Physics

doi:10.1016/j.jalgebra.2009.07.033
fatcat:i7l4lyqszjde5aswg53ewiqlea
*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*...##
###
On the profinite topology of right-angled Artin groups

2008
*
Journal of Algebra
*

Moreover, we investigate the

doi:10.1016/j.jalgebra.2008.03.031
fatcat:qdpqpn2we5euhdwopsjm5ei2nu
*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 . ...##
###
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

2001
*
Journal of Algebra
*

As an application, it is shown that any finite abelian

doi:10.1006/jabr.2001.8915
fatcat:4s3w6xq2rvglzcic2q6xh65lia
*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*. ...##
###
On hereditarily just infinite profinite groups obtained via iterated wreath products
[article]

2015
*
arXiv
*
pre-print

We study a generalisation

arXiv:1506.00139v1
fatcat:buf5zputi5huxmyg4cuhgqyi44
*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. ...##
###
ON THE TOPOLOGY OF THE NONABELIAN TENSOR PRODUCT OF PROFINITE GROUPS

2016
*
Bulletin of the Korean Mathematical Society
*

The properties

doi:10.4134/bkms.b150297
fatcat:uhln7ohpdzbmbfswsbxusozcrq
*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). ...##
###
LIMIT GROUPS ARE CONJUGACY SEPARABLE

2007
*
International journal of algebra and computation
*

A limit

doi:10.1142/s0218196707003810
fatcat:c43sclwwwjas5ofygskx5csln4
*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. ...##
###
Conjugacy Separability of Amalgamated Free Products of Groups

1996
*
Journal of Algebra
*

adopts the appropriate definition

doi:10.1006/jabr.1996.0035
fatcat:al643cl6lrfqvewtmoninqsm74
*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 . ...##
###
Ascending HNN extensions of polycyclic groups have the same cohomology as their profinite completions
[article]

2010
*
arXiv
*
pre-print

Furthermore, let Ĝ∗̂_̂ϕ̂ be the

arXiv:1009.2645v5
fatcat:5bickx2ssfhnzcudknu7zjd6nq
*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. ...##
###
Protori and Torsion-Free Abelian Groups
[article]

2019
*
arXiv
*
pre-print

A morphism between protori lifts to a

arXiv:1903.08022v1
fatcat:np7ietgsdzbqdewvuyxvtgnorq
*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. ...##
###
Profinite extensions of centralizers and the profinite completion of limit groups
[article]

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. ...

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