ON EQUALITY OF ABSOLUTE CENTRAL AND CLASS PRESERVING AUTOMORPHISMS OF FINITE p-GROUPS

Document Type : Original Manuscript

Author

Department of Mathematics, Payame Noor University (PNU), P.O.Box 19395-3697, Tehran, Iran.

Abstract

Let

G

be a finite non-abelian

p

-group and

L (G)

denotes the absolute center of

G

. Also, let

\Aut^{L} (G)

and

\Aut_{c} (G)

denote the group of all absolute central and the class preserving automorphisms of

G

, respectively. In this paper, we give a necessary and sufficient condition for

G

such that

\Aut_{c} (G) = \Aut^{L} (G)

. We also characterize all finite non-abelian

p

-groups of order

p^{n} (n \leq 5)

, for which every absolute central automorphism is class preserving.

Keywords