On relative normal complements in finite groups. II

Leonard, Henry S.

doi:10.1090/S0002-9939-1983-0695243-6

On relative normal complements in finite groups. II
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by Henry S. Leonard PDF

Proc. Amer. Math. Soc. 88 (1983), 212-214 Request permission

Abstract:

Given a finite group $G$ and subgroups $H$ and ${H_0}$ with ${H_0} \triangleleft H$, we let $\pi$ denote the set of prime divisors of $(H:{H_0})$, and we denote this configuration by $(G,H,{H_0},\pi )$. Pamela Ferguson has shown that if $H/{H_0}$ is solvable, then under certain conditions there exists a unique relative normal complement ${G_0}$ of $H$ over ${H_0}$. In this paper we give alternative proofs of her two theorems.

References

Pamela A. Ferguson, Relative normal complements in finite groups, Proc. Amer. Math. Soc. 87 (1983), no. 1, 38–40. MR 677226, DOI 10.1090/S0002-9939-1983-0677226-5
Henry S. Leonard Jr., On relative normal complements in finite groups, Arch. Math. (Basel) 40 (1983), no. 2, 97–108. MR 720899, DOI 10.1007/BF01192757
William F. Reynolds, Isometries and principal blocks of group characters, Math. Z. 107 (1968), 264–270. MR 236280, DOI 10.1007/BF01110015