Volume 11, Issue 4 (2-2026)
mmr 2026, 11(4): 57-65 |
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Orfi R, Fouladi S. Maximal Subsets of Pairwise Non-Commuting Elements in Finite $A_2$-Groups. mmr 2026; 11 (4) :57-65
URL: http://mmr.khu.ac.ir/article-1-3469-en.html
URL: http://mmr.khu.ac.ir/article-1-3469-en.html
1- Kharazmi University , orfi@khu.ac.ir
2- Kharazmi University
2- Kharazmi University
Abstract: (131 Views)
Let $G$ be a finite group. A subset $X subseteq G$ is called a pairwise non-commuting set if $xy neq yx$ for all distinct elements $x, y in X$. If $|X| geq |Y|$ for every other pairwise non-commuting set $Y$ in $G$, then $X$ is called a maximal pairwise non-commuting set. A $p$-group $G$ is defined as an $A_2$-group if it contains a nonabelian subgroup of index $p$ such that all subgroups of index $p^2$ are abelian. In this paper, we determine the exact maximum size of such sets in finite $A_2$-groups.
Type of Study: S |
Subject:
alg
Received: 2025/12/10 | Revised: 2026/02/26 | Accepted: 2025/12/30 | Published: 2026/02/26 | ePublished: 2026/02/26
Received: 2025/12/10 | Revised: 2026/02/26 | Accepted: 2025/12/30 | Published: 2026/02/26 | ePublished: 2026/02/26
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