We show that if G is a finite simple nonabelian group and H is a subgroup of Aut(G) containing G, then the number of conjugacy classes of complements of G in H is strictly smaller than |G|.
A. Lucchini, F. Menegazzo, M. Morigi (2004). Complements of the socle in almost simple groups. RENDICONTI DEL SEMINARIO MATEMATICO DELL'UNIVERSITA' DI PADOVA, 112, 141-163.
Complements of the socle in almost simple groups
MORIGI, MARTA
2004
Abstract
We show that if G is a finite simple nonabelian group and H is a subgroup of Aut(G) containing G, then the number of conjugacy classes of complements of G in H is strictly smaller than |G|.File in questo prodotto:
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