𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Tree Products of Conjugacy Separable Groups

✍ Scribed by P.C. Wong; C.K. Tang

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
345 KB
Volume
222
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

A group G is said to be conjugacy separable if for each pair of elements x y ∈ G such that x and y are not conjugate in G, there exists a finite homomorphic image Ḡ of G such that the images of x y are not conjugate in Ḡ. In this note, we show that the tree products of finitely many conjugacy separable and subgroup separable groups amalgamating central subgroups with trivial intersections are conjugacy separable. We then apply our results to polycyclic-by-finite groups and free-by-finite groups.

📜 SIMILAR VOLUMES

On Generalised Free Products of Conjugac
On Generalised Free Products of Conjugacy Separable Groups
✍ Goansu Kim; James Mccarron; C.Y. Tang 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 196 KB

In this paper we prove that a free product of conjugacy separable groups A and B, amalgamating a cyclic subgroup, is conjugacy separable if A and B are subgroup separable, cyclic conjugacy separable, 2-free, and residually p-finite, for all prime numbers p. The following result is an example of the

A Criterion for the Conjugacy Separabili
A Criterion for the Conjugacy Separability of Amalgamated Free Products of Conjugacy Separable Groups
✍ Goansu Kim; C.Y. Tang 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 293 KB

We first prove a criterion for the conjugacy separability of generalized free products of two conjugacy separable groups amalgamating a cyclic subgroup. Applying this result, we show that tree products of a finite number of conjugacy separable, residually finitely generated torsion-free nilpotent gr

Conjugacy Separability of Amalgamated Fr
Conjugacy Separability of Amalgamated Free Products of Groups
✍ Luis Ribes; Pavel A. Zalesskii 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 310 KB

G and G amalgamating a common subgroup H. The first problem that 1 2 one encounters is that the residual finiteness of G and G does not imply 1 2 w x in general that G is residually finite. Baumslag 1 proved that if G and 1 G are either both free or both torsion-free finitely generated nilpotent 2 g

Separability Properties of Certain Tree
Separability Properties of Certain Tree Products of Groups
✍ Goansu Kim; C.Y. Tang 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 230 KB

We introduce the concept of finite compatibility to prove certain double coset separability of tree products of central subgroup separable groups. We also prove a criterion for the conjugacy separability of generalized free products of two conjugacy separable groups amalgamating a central subgroup i

A Criterion for the Conjugacy Separabili
A Criterion for the Conjugacy Separability of Certain HNN Extensions of Groups
✍ Goansu Kim; C.Y. Tang 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 204 KB

We first prove the double coset separability of certain HNN extensions with cyclic associated subgroups. Using this we prove a criterion for the conjugacy separability of HNN extensions of conjugacy separable groups with cyclic associated subgroups. Applying this result we show that certain HNN exte

Conjugacy in Groups of Upper Triangular
Conjugacy in Groups of Upper Triangular Matrices
✍ I.M Isaacs; Dikran Karagueuzian 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 140 KB

We show that in the group U ‫ކ‬ , a Sylow 2-subgroup of GL ‫ކ‬ , there are elements not conjugate to their inverses if n G 13. It follows that there are irreducible characters of this group that are not real-valued, and that a conjecture of Kirillov is not correct as stated. We give a partial expla