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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


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
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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