Conditions for Sylow 2-subgroups of the Fixed Point Subgroup Implying Solubility

Abstract

AbstractLet A and G be finite groups and suppose that A acts via automorphisms on G with $(|A|, |G|)=1$. We study how certain conditions on the Sylow 2-subgroups of the fixed point subgroup of the action $C_G(A)$ may imply the non-simplicity or solubility of G.