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

Publication Title

Transactions of the American Mathematical Society

ISSN

0002-9947

Divisions

MathematicalSciences

Volume

258

Issue

2

Publisher

American Mathematical Society

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