Maximal subsets of pairwise non-commuting elements of $p$-groups of order less than $p^6$

Document Type: Research Paper

Author

University of Arak

Abstract

Let $G$ be a non-abelian group of order $p^n$‎, ‎where $n\leq 5$ in which $G$ is not extra special of order $p^5$‎. ‎In this paper we determine the maximal size of subsets $X$ of $G$‎ ‎with the property that $xy\neq yx$ for any $x,y$ in $X$ with‎ ‎$x\neq y$‎.

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