Glasnik Matematicki, Vol. 44, No.2 (2009), 343-348.

ON AUTOMORPHISMS OF ORDER p OF METACYCLIC p-GROUPS WITHOUT CYCLIC SUBGROUPS OF INDEX p

Yakov Berkovich

Abstract.   Let L be a metacyclic p-group, p > 2, without cyclic subgroups of index p and let a Aut(L) be of order p. We show that either a centralizes Ω₁(L) or p = 3 and the natural semidirect product < a > · L is of maximal class so the subgroup L has very specific structure. This improves a result by Meierfrankenfeld and Stellmacher.

2000 Mathematics Subject Classification.   20D15.

Key words and phrases.   Metacyclic, minimal nonmetacyclic and minimal nonabelian p-groups, p-groups of maximal class.

DOI: 10.3336/gm.44.2.07

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