$p$-groups with maximal elementary abelian subgroups of rank $2$

Glauberman, George and Mazza, Nadia (2010) $p$-groups with maximal elementary abelian subgroups of rank $2$. Journal of Algebra, 323 (6). pp. 1729-1737. ISSN 0021-8693

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Let p be an odd prime number and G a finite p-group. We prove that if the rank of G is greater than p, then G has no maximal elementary abelian subgroup of rank 2. It follows that if G has rank greater than p, then the poset of elementary abelian subgroups of G of rank at least 2 is connected and the torsion-free rank of the group of endotrivial kG-modules is one, for any field k of characteristic p. We also verify the class-breadth conjecture for the p-groups G whose poset has more than one component.

Item Type: Journal Article
Journal or Publication Title: Journal of Algebra
Additional Information: The final, definitive version of this article has been published in the Journal, Journal of Algebra 323 (6), 2010, © ELSEVIER.
Uncontrolled Keywords: /dk/atira/pure/researchoutput/libraryofcongress/qa
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 33515
Deposited By: Mr Richard Ingham
Deposited On: 25 May 2010 15:26
Refereed?: Yes
Published?: Published
Last Modified: 17 Feb 2020 01:22
URI: https://eprints.lancs.ac.uk/id/eprint/33515

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