Groups with some central automorphisms fixing the central kernel quotient

Document Type : Research Paper

Author

Department of Mathematics, Payame Noor University (PNU), Iran

Abstract

Let G be a group. An automorphism α of a group G is called a central automorphism, if x1xαZ(G) for all xG. Let Lc(G) be the central kernel of G, that is the set of elements of G fixed by all central  automorphisms of G and AutLc(G) denote the group of all central automorphisms of G fixing G/Lc(G) element-wise. In the present paper, we investigate the properties of such automorphisms. Moreover, a full classification of p-groups G of order at most p5 where AutLc(G)=Inn(G) is also given.

Keywords


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