Finitely generated groups L with L ≈ L × M, M ≠ 1, M finitely presented

A Reidemeister-schreier Theorem for Finitely L-presented Groups

We prove a variant of the well-known Reidemeister-Schreier Theorem for finitely L-presented groups. More precisely, we prove that each finite index subgroup of a finitely L-presented group is itself finitely L-presented. Our proof is constructive and it yields a finite L-presentation for the subgroup. We further study conditions on a finite index subgroup of an invariantly finitely L-presented ...

Finitely generated nilpotent groups are finitely presented and residually finite

Definition 1. Let G be a group. G is said to be residually finite if the intersection of all normal subgroups of G of finite index in G is trivial. For a survey of results on residual finiteness and related properties, see Mag-nus, Karrass, and Solitar [6, Section 6.5]. We shall present a proof of the following well known theorem, which is important for Kharlampovich [4, 5]. See also O. V. Bele...

Decompositions of finitely generated and finitely presented groups

In this paper we discuss the splitting or decomposing of finitely generated groups into free products, free products with amalgamation or HNN extensions and we discuss the JSJ decomposition of finitely presented groups.

M ay 2 00 4 Subgroups of finitely presented groups with solvable conjugacy problem

We prove that every countable group with solvable power problem embeds into a finitely presented 2-generated group with solvable power and conjugacy problems.

. , Oates , M . E . , Holmes , M . L . , Knaupp