Groups with Boundedly Finite Conjugacy Classes of Commutators
Abstract
In 1954 B. H. Neumann discovered that if G is a group in which all conjugacy classes are finite with bounded size, then the derived group G' is finite. Later (in 1957) Wiegold found an explicit bound for the order of G'. We study groups in which the conjugacy classes containing commutators are finite with bounded size. We obtain the following results. Let G be a group and n a positive integer. If |x^G|<n for any commutator x in G, then the second derived group G" is finite with n-bounded order. If |x^{G'}|<n for any commutator x in G, then the order of \gamma_3(G') is finite and -bounded. Here \gamma_3(G') is the third term of the lower central series of G'.
Cite
@article{arxiv.1702.02224,
title = {Groups with Boundedly Finite Conjugacy Classes of Commutators},
author = {Glaucia Dierings and Pavel Shumyatsky},
journal= {arXiv preprint arXiv:1702.02224},
year = {2018}
}
Comments
In introduction a comment about explicit bounds is added. The paper will be published in the Quaterly Journal of Math