Lancaster EPrints

$p$-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

[img]
Preview
PDF (gm.pdf)
Download (172Kb) | Preview

    Abstract

    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: 09 Oct 2013 12:44
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/33515

    Actions (login required)

    View Item