Let G be a group. An automorphism α of G is said to be a cyclic automorphism if the subgroup 〈x, xα 〉 is cyclic for every element x of G. In [F. de Giovanni, M.L. Newell, A. Russo: On a class of normal endomorphisms of groups, J. Algebra and its Applications 13, (2014), 6pp] the authors proved that every cyclic automorphism is central, namely, that every cyclic automorphism acts trivially on the factor group G/Z(G). In this paper, the class FW of groups in which every element induces by conjugation a cyclic automorphism on a (normal) subgroup of finite index will be investigated.
On Groups in Which Many Automorphisms Are Cyclic / Brescia, M.; Russo, A.. - In: MATHEMATICS. - ISSN 2227-7390. - 10:2(2022), p. 262. [10.3390/math10020262]
On Groups in Which Many Automorphisms Are Cyclic
Brescia M.Primo
;
2022
Abstract
Let G be a group. An automorphism α of G is said to be a cyclic automorphism if the subgroup 〈x, xα 〉 is cyclic for every element x of G. In [F. de Giovanni, M.L. Newell, A. Russo: On a class of normal endomorphisms of groups, J. Algebra and its Applications 13, (2014), 6pp] the authors proved that every cyclic automorphism is central, namely, that every cyclic automorphism acts trivially on the factor group G/Z(G). In this paper, the class FW of groups in which every element induces by conjugation a cyclic automorphism on a (normal) subgroup of finite index will be investigated.File | Dimensione | Formato | |
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