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$p$-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: 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: Finite p-groups ; Elementary abelian p-subgroups ; Endotrivial modules ; Class-breadth conjecture
    Subjects: Q Science > QA Mathematics
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 33515
    Deposited By: Mr Richard Ingham
    Deposited On: 25 May 2010 16:26
    Refereed?: Yes
    Published?: Published
    Last Modified: 04 Nov 2015 01:47
    Identification Number:

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