Cyclic extensions of parafree groups

Document Type

Article

Publication Date

4-1-1980

Abstract

Let 1 —> F —> G —> T —> 1 be a short exact sequence where F is parafree and T is infinite cyclic. We examine some properties of G when F/F' is a free Zr-module. Here F' is the commutator subgroup of F and ZT is the integral group ring of T. In particular, we show G is parafree and y„F/y„+ XF is a free Z7"-module for every n > 1 (where ynF is the nth term of the lower central series of F).

Keywords

Cyclic extensions, Parafree groups

Divisions

MathematicalSciences

Publication Title

Transactions of the American Mathematical Society

Volume

258

Issue

2

Publisher

American Mathematical Society

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