Eaton, Charles W.
(2005)
*Vertices for irreducible characters of a class of blocks.*
Journal of Algebra, 286 (2).
pp. 492-499.
ISSN 0021-8693

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## Abstract

We observe that Navarro's definition of a vertex for an irreducible character of a $p$-solvable group may be extended to irreducible characters in $p$-blocks with defect groups contained in a normal $p$-solvable subgroup, and show that this definition is independent of the choice of $N$. We show that the fundamental properties of Navarro's vertices generalize, and as a corollary show that the vertices of the irreducible Brauer characters in blocks of the above form are radical and are intersections of pairs of Sylow $p$-subgroups.

Item Type: | Article |
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Uncontrolled Keywords: | finite groups, representation theory, character theory, vertex, simple module |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations |

Depositing User: | Dr Charles Eaton |

Date Deposited: | 27 Oct 2005 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/22 |

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