Maximal subsets of pairwise non-commuting elements of some finite p-groups

Document Type: Research Paper

Authors

1 Arak University, Iran

2 Kharazmi University, Iran

Abstract

Let G be a group. A subset X of G is a set of pairwise noncommuting
elements if xy ̸= yx for any two distinct elements x and y in X.
If |X| ≥ |Y | 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.
In this paper we determine the cardinality of a maximal subset of pairwise
non-commuting elements in any non-abelian p-groups with central quotient
of order less than or equal to p3 for any prime number p. As an immediate
consequence we give this cardinality for any non-abelian group of order p4.

Keywords

Main Subjects