On products of two nilpotent subgroups of a finite group |
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Authors: | Arie Bialostocki |
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Institution: | 1. Department of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel
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Abstract: | LetG be a finite group with an abelian Sylow 2-subgroup. LetA be a nilpotent subgroup ofG of maximal order satisfying class (A)≦k, wherek is a fixed integer larger than 1. Suppose thatA normalizes a nilpotent subgroupB ofG of odd order. ThenAB is nilpotent. Consequently, ifF(G) is of odd order andA is a nilpotent subgroup ofG of maximal order, thenF(G)?A. |
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