Groups, Geometry, and Dynamics


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Volume 1, Issue 4, 2007, pp. 585–611
DOI: 10.4171/GGD/25

Published online: 2007-12-31

Complements of the socle in monolithic groups

Andrea Lucchini[1], Federico Menegazzo[2] and Marta Morigi[3]

(1) Università di Padova, Italy
(2) Università di Padova, Italy
(3) Università di Bologna, Italy

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|.

Keywords: Monolithic groups, complements, finite simple groups

Lucchini Andrea, Menegazzo Federico, Morigi Marta: Complements of the socle in monolithic groups. Groups Geom. Dyn. 1 (2007), 585-611. doi: 10.4171/GGD/25