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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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 |
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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 Apr 2016 01:10 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/33515 |

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