Construction of finite p-groups with prescribed group of noncentral automorphisms (Q1085274)

Liebeck and the reviewer have used graphs for the construction of p- groups G of class two such that a given group K, acting as semiregular permutation group on the basis of G/G' is isomorphic to Aut G/Aut\({}_ c G\). The author shows that the graph can be chosen such that the action is regular if K is isomorphic to \(S_ n\) with \(n>4\), to \(A_ n\) with \(n>5\), to \(C_ 5 wr C_ 5\), and to PGL(2,p) or PSL(2,p) with \(p\geq 13\). For the latter cases a general statement on the existence of a suitable graph for groups \(K=<x,y>\) with conditions on certain product orders is needed (Lemma 5.1.1).