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]](http://eprints.lancs.ac.uk/style/images/fileicons/application_pdf.png)
| PDF (gm.pdf) Download (172Kb) | Preview |
Official URL: http://dx.doi.org/10.1016/j.jalgebra.2009.10.015
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: | 26 Jul 2012 17:25 |
| Identification Number: | |
| URI: | http://eprints.lancs.ac.uk/id/eprint/33515 |
Actions (login required)
| View Item |
