Geodesic
Irreducible Automorphisms of Certain p-Groups
Canadian journal of mathematics, Tome 29 (1977) no. 2, pp. 333-348

Voir la notice de l'article provenant de la source Cambridge University Press

The chief purpose of this paper is to find all pairs (G, θ) where G is a finite special p-group, and θ is an automorphism of G acting trivially on the Frattini subgroup and irreducibly on the Frattini quotient. This problem arises in the context of describing finite groups having an abelian maximal subgroup. In fact, we solve a more general problem for a wider class of p-groups, which we call special F-groups, where F is a finite field of characteristic p. We point out that if p is odd, then an F-group has exponent p. On the other hand, every special 2-group is also a special GF(2)-group. 
Djoković, D. Ž.; Malzan, J. Irreducible Automorphisms of Certain p-Groups. Canadian journal of mathematics, Tome 29 (1977) no. 2, pp. 333-348. doi: 10.4153/CJM-1977-037-8
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