Finitely annihilated groups

Authors

  • M. Chiodo University of Neuchatel

Keywords:

coverings of groups, weight of finite groups

Abstract

In 1976, Wiegold asked if every finitely generated perfect group has weight 1. We introduce a new property of groups, finitely annihilated, and show that this might be a possible approach to resolving Wiegold’s problem. For finitely generated groups, we show that in several classes (finite, solvable, free), being finitely annihilated is equivalent to having noncyclic abelianisation. However, we also construct an infinite family of (finitely presented) finitely annihilated groups with cyclic abelianisation. We apply our work to show that the weight of a nonperfect finite group, or a nonperfect finitely generated solvable group, is the same as the weight of its abelianisation. This recovers the known partial results on the Wiegold problem: a finite (or finitely generated solvable) perfect group has weight 1. DOI:- 10.1017/S0004972714000355

Author Biography

M. Chiodo, University of Neuchatel

Postdoctoral researcher, department of mathematics.

Published

2014-09-20

Issue

Section

Articles