# Pairwise‎ ‎non-commuting elements in finite metacyclic $2$-groups and some finite $p$-groups

Document Type : Research Paper

Author

Abstract

Let $G$ be a finite group‎. ‎A subset $X$ of $G$ is a set of pairwise non-commuting elements‎
‎if any two distinct elements of $X$ do not commute‎. ‎In this paper‎
‎we determine the maximum size of these subsets in any finite‎
‎non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup‎.

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### History

• Receive Date: 01 August 2013
• Revise Date: 30 November 2013
• Accept Date: 01 December 2013