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Zbl 0607.20018
Soules, Panagiotis C.
Construction of finite p-groups with prescribed group of noncentral automorphisms. (English)
[J] Rend. Semin. Mat. Univ. Padova 76, 75-88 (1986). ISSN 0041-8994

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${}\sb c G$. The author shows that the graph can be chosen such that the action is regular if K is isomorphic to $S\sb n$ with $n>4$, to $A\sb n$ with $n>5$, to $C\sb 5 wr C\sb 5$, and to PGL(2,p) or PSL(2,p) with $p\ge 13$. 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).
[H.Heineken]

MSC 2000:: *20F28 Automorphism groups of groups
20D45 Automorphisms of finite groups
05C25 Graphs and groups
20D15 Nilpotent finite groups
20B25 Finite automorphism groups of miscellaneous structures
20F29 Representations of groups as automorphism groups of alg. systems

Keywords: non-central automorphisms; graphs; p-groups

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