On cyclic automorphisms of a group-Reference-Cited by-同舟云学术

On cyclic automorphisms of a group

Published:2020-07-04 Issue:10 Volume:20 Page:
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Brescia Mattia¹,Russo Alessio²^ORCID

Affiliation:

1. Dipartimento di Matematica e Applicazioni, Università Degli Studi di Napoli Federico II, Corso Umberto I, 40, Napoli, Italy

2. Dipartimento di Matematica e Fisica, Università Della Campania “Luigi Vanvitelli”, Viale Lincoln 5, Caserta, Italy

Abstract

An endomorphism [Formula: see text] of a group [Formula: see text] is called a cyclic endomorphism if the subgroup [Formula: see text] is cyclic for all elements [Formula: see text] of [Formula: see text]. It can be proved that every cyclic endomorphism is normal, i.e. it commutes with every inner automorphism of [Formula: see text] (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 [Formula: see text] in which the group [Formula: see text] of cyclic automorphisms has finite index in [Formula: see text] will be investigated.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498821501838

Reference12 articles.

1. Power automorphisms of a group

2. E3039

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On groups with many subgroups satisfyinga transitive normality relation;NOTE MAT;2024

2. Central Endomorphisms of Groups and Radical Rings;ADV GROUP THEOR APPL;2023

3. ON THE CENTRAL KERNEL OF A GROUP;Bulletin of the Australian Mathematical Society;2022-10-13

4. On Groups in Which Many Automorphisms Are Cyclic;Mathematics;2022-01-15

5. Generalized norms of groups: retrospective review and current status;Algebra and Discrete Mathematics;2022