Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-27T02:49:13.904Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected])
R. ORFI*
Affiliation:
Department of Mathematics, University of Arak, Arak, Iran (email: [email protected])
*
✉For correspondence; e-mail: reza˙[email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
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

References

[1]Abdollahi, A., Akbari, A. and Maimani, H. R., ‘Non-commuting graph of a group’, J. Algbera 298(2) (2006), 468–492.CrossRefGoogle Scholar
[2]Azad, A. and Praeger, C. E., ‘Maximal subsets of pairwise non-commuting elements of three-dimensional general linear groups’, Bull. Aust. Math. Soc. 80(1) (2009), 91–104.CrossRefGoogle Scholar
[3]Bertram, E. A., ‘Some applications of graph theory to finite groups’, Discrete Math. 44(1) (1983), 31–43.CrossRefGoogle Scholar
[4]Chin, A. M. Y., ‘On non-commuting sets in an extraspecial p-group’, J. Group Theory 8(2) (2005), 189–194.CrossRefGoogle Scholar
[5] The GAP Group, ‘GAP – Groups, Algorithms, and Programming’, Version 4.4.12, 2008, http://www.gap-system.org.Google Scholar
[6]Huppert, B., Endliche Gruppen, I (Springer, Berlin, 1967).CrossRefGoogle Scholar
[7]Leedham-Green, C. R. and McKay, S., The Structure of Groups of Prime Power Order, London Mathematical Society Monographs, New Series, 27 (Oxford University Press, Oxford, 2002).CrossRefGoogle Scholar
[8]Neumann, B. H., ‘A problem of Paul Erdős on groups’, J. Aust. Math. Soc. Ser. A 21(4) (1976), 467–472.CrossRefGoogle Scholar
[9]Rocke, D. M., ‘p-groups with abelian centralizers’, Proc. Lond. Math. Soc. 30(3) (1975), 55–57.CrossRefGoogle Scholar