Bounding an Index by the Largest Character Degree of a p-Solvable Group |
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| Authors: | Mark L. Lewis |
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| Affiliation: | 1. Department of Mathematical Sciences , Kent State University , Kent , Ohio , USA lewis@math.kent.edu |
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| Abstract: | In this article, we show that if p is a prime and G is a p-solvable group, then |G: O p (G)| p ≤ (b(G) p /p)1/(p?1), where b(G) is the largest character degree of G. If p is an odd prime that is not a Mersenne prime or if the nilpotence class of a Sylow p-subgroup of G is at most p, then |G: O p (G)| p ≤ b(G). |
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| Keywords: | Character degree Index p-Radical |
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