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

Archiv der Mathematik ◽

10.1007/s00013-015-0727-8 ◽

2015 ◽

Vol 104 (2) ◽

pp. 101-109 ◽

Cited By ~ 2

Author(s):

S. C. Chagas ◽

P. A. Zalesskii

Keyword(s):

Finite Groups ◽

Conjugacy Separability

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Conway and iteration hemirings Part 1

International Journal of Algebra and Computation ◽

10.1142/s0218196714500210 ◽

2014 ◽

Vol 24 (04) ◽

pp. 461-482

Author(s):

M. Droste ◽

Z. Ésik ◽

W. Kuich

Keyword(s):

Finite Groups ◽

Transition Systems ◽

Free Constructions ◽

The Relationship

Conway hemirings are Conway semirings without a multiplicative unit. We also define iteration hemirings as Conway hemirings satisfying certain identities associated with the finite groups. Iteration hemirings are iteration semirings without a multiplicative unit. We provide an analysis of the relationship between Conway hemirings and (partial) Conway semirings and describe several free constructions. In the second part of the paper we define and study hemimodules of Conway and iteration hemirings, and show their applicability in the analysis of quantitative aspects of the infinitary behavior of weighted transition systems. These include discounted and average computations of weights investigated recently.

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