On Finite n-Acentralizer Groups |
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Authors: | Mohammad Mehdi Nasrabadi Ali Gholamian |
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Affiliation: | 1. Department of Mathematics , University of Birjand , Birjand , Iran mnasrabadi@birjand.ac.ir;3. Department of Mathematics , University of Birjand , Birjand , Iran |
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Abstract: | Let G be a group and Aut(G) be the group of automorphisms of G. Then the Acentralizer of an automorphism α ∈Aut(G) in G is defined as C G (α) = {g ∈ G∣α(g) = g}. For a finite group G, let Acent(G) = {C G (α)∣α ∈Aut(G)}. Then for any natural number n, we say that G is n-Acentralizer group if |Acent(G)| =n. We show that for any natural number n, there exists a finite n-Acentralizer group and determine the structure of finite n-Acentralizer groups for n ≤ 5. |
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Keywords: | Automorphism Centralizer Finite groups |
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