## 2005.11: Vertices for irreducible characters of a class of blocks

2005.11:
Charles W. Eaton
(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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DOI: doi:10.1016/j.jalgebra.2005.01.007

## 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 2000 > 20 Group theory and generalizations |

MIMS number: | 2005.11 |

Deposited By: | Dr Charles Eaton |

Deposited On: | 27 October 2005 |

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