On relative normal complements in finite groups. III

Author:
Henry S. Leonard

Journal:
Proc. Amer. Math. Soc. **95** (1985), 5-6

MSC:
Primary 20D40

MathSciNet review:
796435

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Abstract: Let be a finite group, let , and let be the set of prime divisors of . Assume that whenever two elements of are -conjugate then they are -conjugate. Assume that for all , is a -number. We prove that is a -Hall subgroup and that there exists a normal complement . An example shows that the generalization to relative normal complements is not true.

**[1]**Richard Brauer,*On quotient groups of finite groups*, Math. Z.**83**(1964), 72–84. MR**0159872****[2]**Henry S. Leonard Jr.,*On relative normal complements in finite groups*, Arch. Math. (Basel)**40**(1983), no. 2, 97–108. MR**720899**, 10.1007/BF01192757**[3]**Henry S. Leonard Jr.,*On relative normal complements in finite groups. II*, Proc. Amer. Math. Soc.**88**(1983), no. 2, 212–214. MR**695243**, 10.1090/S0002-9939-1983-0695243-6**[4]**Geoffrey R. Robinson,*Blocks, isometries, and sets of primes*, Proc. London Math. Soc. (3)**51**(1985), no. 3, 432–448. MR**805716**, 10.1112/plms/s3-51.3.432

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DOI:
https://doi.org/10.1090/S0002-9939-1985-0796435-X

Article copyright:
© Copyright 1985
American Mathematical Society