Vertices of simple modules and normal subgroups ofp-solvable groups |
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Authors: | A Laradji |
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Affiliation: | (1) Department of Mathematics College of Science, King Saud University, P.O. Box 2455, 11451 Riyadh, Saudi Arabia |
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Abstract: | Let π be a set of prime numbers andG a finite π-separable group. Let θ be an irreducible π′-partial character of a normal subgroupN ofG and denote by Iπ′ (G‖θ), the set of all irreducible π′-partial characters Φ ofG such that θ is a constituent of ΦN. In this paper, we obtain some information about the vertices of the elements in Iπ′ (G‖θ). As a consequence, we establish an analogue of Fong's theorem on defect groups of covering blocks, for the vertices of
the simple modules (in characteristicsp) of a finitep-solvable group lying over a fixed simple module of a normal subgroup. |
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Keywords: | 20C15 20C20 |
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