Computing with subgroups of automorphism groups of finite groups

Let Cay(G,S) be a connected tetravalent Cayley graph on a regular p-group G and let Aut(G) be the automorphism group of G. In this paper, it is proved that, for each prime p<>2,5, the automorphism group of the Cayley graph Cay(G,S) is the semidirect ...

Let Z be a complete set of Sylow subgroups of a finite group G, that is, for each prime p dividing the order of G, Z contains one and only one Sylow p-subgroup of G. A subgroup H of G is said to be Z-permutable in G if H permutes with every member of Z. ...

A primitive non-regular permutation group is called extremely primitive if a point stabilizer acts primitively on each of its nontrivial orbits. This notation was first introduced in the work of Manning in the 1920s. In 1988, Delandtsheer and ...$\mathrm{}$$\frac{{}^{\mathrm{}}\mathrm{}}{\mathrm{}}$