Automorphisms of nonsplit extensions of 2-groups by $PS{L}_2(q)$

Abstract

We complete the description of automorphism groups of all nonsplit extensions of elementary abelian $2$-groups by $PS{L}_2(q)$, with $q$ odd, for an irreducible induced action. An application of this result to the theory of $\pi$-submaximal subgroups is given.

References in corpus (5)

• Classification and properties of the $\pi$-submaximal subgroups in minimal nonsolvable groups
• The proper definition and Wielandt-Hartley's theorem for submaximal $\mathfrak{X}$-subgroups
• The reduction theorem for relatively maximal subgroups
• On the behavior of $\pi$-submaximal subgroups under homomorphisms
• The behavior of $\pi$-submaximal subgroups under homomorphisms with $\pi$-separable kernels