Subgroup conjugacy separability of free-by-finite groups

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.

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Conjugacy Separability of Generalized Free Products of Certain Conjugacy Separable Groups

Canadian Mathematical Bulletin ◽

10.4153/cmb-1995-017-5 ◽

1995 ◽

Vol 38 (1) ◽

pp. 120-127 ◽

Cited By ~ 17

Author(s):

C. Y. Tang

Keyword(s):

Finite Groups ◽

Cyclic Subgroup ◽

Finitely Generated ◽

Free Products ◽

Conjugacy Separability ◽

Conjugacy Separable ◽

Generalized Free Products

AbstractWe prove that generalized free products of finitely generated free-byfinite or nilpotent-by-finite groups amalgamating a cyclic subgroup areconjugacy separable. Applying this result we prove a generalization of a conjecture of Fine and Rosenberger [7] that groups of F-type are conjugacy separable.

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On the conjugacy separability of some free constructions of groups by root classes of finite groups

Mathematical Notes ◽

10.1134/s0001434615050132 ◽

2015 ◽

Vol 97 (5-6) ◽

pp. 779-790 ◽

Cited By ~ 2

Author(s):

E. V. Sokolov

Keyword(s):

Finite Groups ◽

Conjugacy Separability ◽

Free Constructions

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Residual finiteness, subgroup separability and conjugacy separability of certain HNN extensions

Mathematica Slovaca ◽

10.2478/s12175-012-0052-7 ◽

2012 ◽

Vol 62 (5) ◽

Cited By ~ 1

Author(s):

K. Wong ◽

P. Wong

Keyword(s):

Finite Groups ◽

Finite Subgroup ◽

Residual Finiteness ◽

Residually Finite ◽

Hnn Extensions ◽

Conjugacy Separability ◽

Subgroup Separability ◽

Conjugacy Separable

AbstractIn this note we shall give characterisations for HNN extensions of non-cyclic polycyclic-by-finite groups with normal infinite cyclic associated subgroups to be residually finite, subgroup separable and conjugacy separable.

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