We show that if H is a finite group with a unique minimal normal subgroup N, which is not abelian, then the number of conjugacy classes of complements of N in H is strictly smaller than |N|.
A. Lucchini, F. Menegazzo, M. Morigi (2007). Complements of the socle in monolithic groups. GROUPS, GEOMETRY, AND DYNAMICS, 1, 585-611 [10.4171/GGD/25].
Complements of the socle in monolithic groups
MORIGI, MARTA
2007
Abstract
We show that if H is a finite group with a unique minimal normal subgroup N, which is not abelian, then the number of conjugacy classes of complements of N in H is strictly smaller than |N|.File in questo prodotto:
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