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https://doi.org/10.3336/gm.44.2.07

On automorphisms of order p of metacyclic p-groups without cyclic subgroups of index p

Yakov Berkovich ; Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel

Sažetak

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.

Ključne riječi

Metacyclic; minimal nonmetacyclic and minimal nonabelian p-groups; p-groups of maximal classs

Hrčak ID:

44051

URI

https://hrcak.srce.hr/44051

Datum izdavanja:

9.12.2009.

Posjeta: 1.184 *