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ON MAXIMAL SUBSETS OF PAIRWISE NONCOMMUTING ELEMENTS IN FINITE
$p$-GROUPS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 92 / Issue 3 / December 2015
- Published online by Cambridge University Press:
- 20 August 2015, pp. 380-389
- Print publication:
- December 2015
-
- Article
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A subset
$X$ of a finite group 
$G$ is a set of pairwise noncommuting elements if 
$xy\neq yx$ for all 
$x\neq y\in X$. If 
$|X|\geq |Y|$ for any other subset 
$Y$ of pairwise noncommuting elements, then 
$X$ is called a maximal subset of pairwise noncommuting elements and the size of such a set is denoted by 
${\it\omega}(G)$. In a recent article by Azad et al. [‘Maximal subsets of pairwise noncommuting elements of some finite 
$p$-groups’, Bull. Iran. Math. Soc.39(1) (2013), 187–192], the value of 
${\it\omega}(G)$ is computed for certain 
$p$-groups 
$G$. In the present paper, our aim is to generalise these results and find 
${\it\omega}(G)$ for some more 
$p$-groups of interest.
