| Abstrakt: |
Let G be a group and let L (G) denote the absolute center of G. An automorphism α of G is called an absolute central automorphism if x − 1 x α ∈ L (G) for each x ∈ G. An automorphism α of G is called a central automorphism if x − 1 x α ∈ Z (G) for each x ∈ G. Also, let G be an autonilpotent finite p -group of class n + 1 , where n ≥ 1. We call an automorphism α of G is an n th autoclass-preserving if for all x ∈ G , there exists an element g x ∈ K n − 1 (G) such that x α = g x − 1 x g x , where K n − 1 (G) is the n − 1 th autocommutator subgroup of G. In this paper, first, we characterize finite p -group G of class 2 such that every central automorphism is absolute central. We also obtain a necessary and sufficient condition for an autonilpotent finite p -group of class n + 1 such that each absolute central automorphism is an n th autoclass-preserving. [ABSTRACT FROM AUTHOR] |
