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, University of Isfahan, Isfahan 81746-73441, Iran
and
School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O.Box: 19395-5746, Tehran, Iran
e-mail: a.abdollahi@math.ui.ac.ir

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 CG(φ)={x∈ G | xφ=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.


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DOI: 10.3336/gm.49.1.10


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