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MAXIMAL SUBSETS OF PAIRWISE NONCOMMUTING ELEMENTS OF SOME p-GROUPS OF MAXIMAL CLASS

Part of: Representation theory of groups

Published online by Cambridge University Press:  19 August 2011

S. FOULADI  and
R. ORFI
S. FOULADI
Affiliation:
Department of Mathematics, University of Arak, Arak, Iran (email: s-fouladi@araku.ac.ir)
R. ORFI*
Affiliation:
Department of Mathematics, University of Arak, Arak, Iran (email: r-orfi@araku.ac.ir)
*
✉For correspondence; e-mail: reza˙orfi@yahoo.com
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Abstract

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Let G be a group. A subset X of G is a set of pairwise noncommuting elements if xy≠yx for any two distinct elements x and y in X. If |X|≥|Y | for any other set of pairwise noncommuting elements Y in G, then X is said to be a maximal subset of pairwise noncommuting elements. In this paper we determine the cardinality of a maximal subset of pairwise noncommuting elements for some p-groups of maximal class. Specifically, we determine this cardinality for all 2 -groups and 3 -groups of maximal class.

Keywords

p-groups of maximal classAC-group

MSC classification

Secondary: 20D15: Nilpotent groups, $p$-groups

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 3 , December 2011 , pp. 447 - 451
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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