On non-commuting sets and centralizers in infinite group
Group Theory
2014-12-16 v1
Abstract
A subset X of a group G is a set of pairwise non-commuting ele- ments if ab 6= ba for any two distinct elements a and b in X. If jXj ? jY j for any other set of pairwise non-commuting elements Y in G, then X is said to be a maximal subset of pairwise non-commuting elements and the cardinality of such a subset is denoted by !(G). In this paper, among other thing, we prove that, for each positive integer n, there are only finitely many groups G, up to isoclinic, with !(G) = n (with exactly n centralizers).
Cite
@article{arxiv.1412.4349,
title = {On non-commuting sets and centralizers in infinite group},
author = {Mohammad Zarrin},
journal= {arXiv preprint arXiv:1412.4349},
year = {2014}
}
Comments
5 pages, to appear, Group Theory, 2015