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Ning Su, Adolfo Ballester-Bolinches, Hangyang Meng.
A note on normal complements for finite groups
Bull. Austral. Math. Soc., 98 (1):109-112, 2018
Assume that G is a finite group and H is a 2-nilpotent Sylow tower Hall subgroup of G such that if x and y are G-conjugate elements of H ∩ G0 of prime order or order 4, then x and y are H-conjugate. We prove hat there exists a normal subgroup N of G such that G = HN and H ∩ N = 1.
2010 Mathematics Subject Classification: primary 20D20; secondary 20D10
Keywords: finite group, conjugation, Hall subgroup, normal complement.