On the exponent of a finite group admitting a fixed-point-free four-group of automorphisms

E. Romano, P. Shumyatsky

Let $A$ be a group isomorphic with either $S_4$, the symmetric group on four symbols, or $D_8$, the dihedral group of order 8. Let $V$ be a normal four-subgroup of $A$ and $\alpha$ an i…