Glasnik Matematicki, Vol. 49, No. 1 (2014), 119-122.

P-GROUPS FOR WHICH EACH OUTER P-AUTOMORPHISM CENTRALIZES ONLY P ELEMENTS

Alireza Abdollahi and S. Mohsen Ghoraishi

Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University, Ahvaz, Iran
and
School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O.Box: 19395-5746, Tehran, Iran
e-mail: ghoraishi@gmail.com & m.ghoraishi@scu.ac.ir

Abstract.   An automorphism of a group is called outer if it is not an inner automorphism. Let G be a finite p-group. Then for every outer p-automorphism φ of G the subgroup C_G(φ)={x∈ G | x^φ=x} has order p if and only if G is of order at most p².

2010 Mathematics Subject Classification.   20D45, 20E36.

Key words and phrases.   p-groups, p-automorphism, outer automorphism.

DOI: 10.3336/gm.49.1.10

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