An endomorphism α of a group G is called a cyclic endomorphism if the subgroup is cyclic for all elements x of G. It can be proved that every cyclic endomorphism is normal, i.e. it commutes with every inner automorphism of G (see [F. de Giovanni, M. L. Newell and A. Russo, On a class of normal endomorphisms of groups, J. Algebra its Appl. 13 (2014) 6pp.]). In this paper, some further properties of cyclic endomorphisms will be pointed out. Moreover, the structure of a group G in which the group CAut(G) of cyclic automorphisms has finite index in Aut(G) will be investigated.
On cyclic automorphisms of a group
Alessio Russo
;
2021
Abstract
An endomorphism α of a group G is called a cyclic endomorphism if the subgroup is cyclic for all elements x of G. It can be proved that every cyclic endomorphism is normal, i.e. it commutes with every inner automorphism of G (see [F. de Giovanni, M. L. Newell and A. Russo, On a class of normal endomorphisms of groups, J. Algebra its Appl. 13 (2014) 6pp.]). In this paper, some further properties of cyclic endomorphisms will be pointed out. Moreover, the structure of a group G in which the group CAut(G) of cyclic automorphisms has finite index in Aut(G) will be investigated.File in questo prodotto:
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