On finite groups whose Sylow subgroups have a bounded number of generators |
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Authors: | Colin D Reid |
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Institution: | 1.Mathematisches Institut,Georg-August Universit?t G?ttingen,G?ttingen,Germany |
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Abstract: | Let G be a finite non-nilpotent group such that every Sylow subgroup of G is generated by at most δ elements, and such that p is the largest prime dividing |G|. We show that G has a non-nilpotent image G/N, such that N is characteristic and of index bounded by a function of δ and p. This result will be used to prove that G has a nilpotent normal subgroup of index bounded in terms of δ and p. |
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