Volume 32, Issue 3
On Non-Commuting Sets in a Finite $p$-Group with Derived Subgroup of Prime Order

Commun. Math. Res., 32 (2016), pp. 193-197.

Published online: 2021-05

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• Abstract

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.

• Keywords

finite $p$-group, non-commuting set, cardinality.

20F18

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@Article{CMR-32-193, author = {Yulei and Wang and and 18516 and and Yulei Wang and Heguo and Liu and and 18517 and and Heguo Liu}, title = {On Non-Commuting Sets in a Finite $p$-Group with Derived Subgroup of Prime Order}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {32}, number = {3}, pages = {193--197}, abstract = {

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} }
TY - JOUR T1 - On Non-Commuting Sets in a Finite $p$-Group with Derived Subgroup of Prime Order AU - Wang , Yulei AU - Liu , Heguo JO - Communications in Mathematical Research VL - 3 SP - 193 EP - 197 PY - 2021 DA - 2021/05 SN - 32 DO - http://doi.org/10.13447/j.1674-5647.2016.03.01 UR - https://global-sci.org/intro/article_detail/cmr/18891.html KW - finite $p$-group, non-commuting set, cardinality. AB -

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.

Yulei Wang & Heguo Liu. (2021). On Non-Commuting Sets in a Finite $p$-Group with Derived Subgroup of Prime Order. Communications in Mathematical Research . 32 (3). 193-197. doi:10.13447/j.1674-5647.2016.03.01
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