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

Document Type : Research Paper


Academic Staff


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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