Commun. Math. Res., 32 (2016), pp. 193-197.
Published online: 2021-05
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Let $G$ be a finite group. A nonempty subset $X$ of $G$ is said to be non-commuting if $xy≠yx$ for any $x, y ∈ X$ with $x≠y$. If $|X| ≥ |Y|$ for any other non-commuting set $Y$ in $G$, then $X$ is said to be a maximal non-commuting set. In this paper, we determine upper and lower bounds on the cardinality of a maximal non-commuting set in a finite $p$-group with derived subgroup of prime order.
}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2016.03.01}, url = {http://global-sci.org/intro/article_detail/cmr/18891.html} }Let $G$ be a finite group. A nonempty subset $X$ of $G$ is said to be non-commuting if $xy≠yx$ for any $x, y ∈ X$ with $x≠y$. If $|X| ≥ |Y|$ for any other non-commuting set $Y$ in $G$, then $X$ is said to be a maximal non-commuting set. In this paper, we determine upper and lower bounds on the cardinality of a maximal non-commuting set in a finite $p$-group with derived subgroup of prime order.