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ON MAXIMAL SUBSETS OF PAIRWISE NONCOMMUTING ELEMENTS IN FINITE $p$-GROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  20 August 2015

M. R. DARAFSHEH ,
M. GHORBANI  and
S. K. PRAJAPATI
M. R. DARAFSHEH*
Affiliation:
School of Mathematics, Statistics, and Computer Science, College of Science, University of Tehran, Tehran, Iran email darafsheh@ut.ac.ir
M. GHORBANI
Affiliation:
Department of Mathematics, Mazandaran University of Science and Technology, P.O. Box 11111, Behshahr, Iran email m_ghorbani@iust.ac.ir
S. K. PRAJAPATI
Affiliation:
Einstein Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem 91904, Israel email skprajapati.iitd@gmail.com
*
✉darafsheh@ut.ac.ir
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Abstract

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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.

Keywords

pairwise noncommuting elementsAC-groupsfinite p-groups

MSC classification

Primary: 20D60: Arithmetic and combinatorial problems
Secondary: 20D15: Nilpotent groups, $p$-groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 3 , December 2015 , pp. 380 - 389
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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