Glasnik matematički, Vol. 44 No. 2, 2009.
Original scientific paper
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
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.
Keywords
Metacyclic; minimal nonmetacyclic and minimal nonabelian p-groups; p-groups of maximal classs
Hrčak ID:
44051
URI
Publication date:
9.12.2009.
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