The complete reducibility of some GF(2)A7-modules

Abstract

It is proved that, if G is a finite group with a nontrivial normal 2-subgroup Q such that G/Q ∼= A 7 and an element of order 5 from G acts freely on Q, then the extension G over Q is splittable, Q is an elementary abelian group, and Q is the direct product of minimal normal subgroups of G each of which is isomorphic, as a G/Q-module, to one of the two 4-dimensional irreducible GF(2)A7-modules that are conjugate with respect to an outer automorphism of the group A7. © 2013 Pleiades Publishing, Ltd.