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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Bialostocki, A. On products of two nilpotent subgroups of a finite group. Israel J. Math. 20, 178–188 (1975). https://doi.org/10.1007/BF02757885
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DOI: https://doi.org/10.1007/BF02757885