scholarly journals Limit groups are subgroup conjugacy separable

2016 ◽  
Vol 461 ◽  
pp. 121-128 ◽  
Author(s):  
Sheila C. Chagas ◽  
Pavel A. Zalesskii
Keyword(s):  
Limit Groups ◽  
Conjugacy Separable

scholarly journals LIMIT GROUPS ARE CONJUGACY SEPARABLE

2007 ◽  
Vol 17 (04) ◽  
pp. 851-857 ◽  
Author(s):  
S. C. CHAGAS ◽  
P. A. ZALESSKII
Keyword(s):  
Free Group ◽  
Finitely Generated ◽  
Limit Group ◽  
Limit Groups ◽  
Conjugacy Separable

A limit group is a finitely-generated subgroup of a fully residually free group. We prove in this paper the result announced in the title.

scholarly journals Quantitative residual properties of Γ-limit groups

2014 ◽  
Vol 24 (02) ◽  
pp. 207-231
Author(s):  
Brent B. Solie
Keyword(s):  
Hyperbolic Group ◽  
Finitely Generated ◽  
Limit Group ◽  
Limit Groups ◽  
Residual Properties

Let Γ be a fixed hyperbolic group. The Γ-limit groups of Sela are exactly the finitely generated, fully residually Γ groups. We introduce a new invariant of Γ-limit groups called Γ-discriminating complexity. We further show that the Γ-discriminating complexity of any Γ-limit group is asymptotically dominated by a polynomial.

scholarly journals Separating conjugates in amalgamated free products and HNN extensions

1980 ◽  
Vol 29 (1) ◽  
pp. 35-51 ◽  
Author(s):  
Joan L. Dyer
Keyword(s):  
Nilpotent Groups ◽  
Conjugacy Classes ◽  
Free Products ◽  
Amalgamated Free Products ◽  
Hnn Extensions ◽  
Nontrivial Center ◽  
One Relator Groups ◽  
Amalgamated Subgroup ◽  
Conjugacy Separable ◽  
Base Group

AbstractA group G is termed conjugacy separable (c.s.) if any pair of distinct conjugacy classes may be mapped to distinct conjugacy classes in some finite epimorph of G. The free product of A and B with cyclic amalgamated subgroup H is shown to be c.s. if A and B are both free, or are both finitely generated nilpotent groups. Further, one-relator groups with nontrivial center and HNN extensions with c.s. base group and finite associated subgroups are also c.s.

Limit groups as limits of free groups

2005 ◽  
Vol 146 (1) ◽  
pp. 1-75 ◽  
Author(s):  
Christophe Champetier ◽  
Vincent Guirardel
Keyword(s):  
Free Groups ◽  
Limit Groups

scholarly journals On pro-p analogues of limit groups via extensions of centralizers

2009 ◽  
Vol 267 (1-2) ◽  
pp. 109-128 ◽  
Author(s):  
D. H. Kochloukova ◽  
P. A. Zalesskii
Keyword(s):  
Limit Groups

Conjugacy Separability of Certain Polygonal Products

1996 ◽  
Vol 39 (3) ◽  
pp. 294-307 ◽  
Author(s):  
Goansu Kim
Keyword(s):  
Finite Groups ◽  
Abelian Groups ◽  
Finitely Generated ◽  
Cyclic Subgroups ◽  
Conjugacy Separability ◽  
Conjugacy Separable

AbstractWe show that polygonal products of polycyclic-by-finite groups amalgamating central cyclic subgroups, with trivial intersections, are conjugacy separable. Thus polygonal products of finitely generated abelian groups amalgamating cyclic subgroups, with trivial intersections, are conjugacy separable. As a corollary of this, we obtain that the group A1 *〈a1〉A2 *〈a2〉 • • • *〈am-1〉Am is conjugacy separable for the abelian groups Ai.

scholarly journals EQUIVARIANT COMPRESSION OF CERTAIN DIRECT LIMIT GROUPS AND AMALGAMATED FREE PRODUCTS

2016 ◽  
Vol 58 (3) ◽  
pp. 739-752
Author(s):  
CHRIS CAVE ◽  
DENNIS DREESEN
Keyword(s):  
Finite Index ◽  
Direct Limit ◽  
Free Products ◽  
Limit Groups ◽  
Amalgamated Free Products

AbstractWe give a means of estimating the equivariant compression of a group G in terms of properties of open subgroups Gi ⊂ G whose direct limit is G. Quantifying a result by Gal, we also study the behaviour of the equivariant compression under amalgamated free products G1∗HG2 where H is of finite index in both G1 and G2.

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