ON A CLASS OF NORMAL ENDOMORPHISMS OF GROUPS-Reference-Cited by-同舟云学术

ON A CLASS OF NORMAL ENDOMORPHISMS OF GROUPS

Published:2013-08-20 Issue:01 Volume:13 Page:1350061
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

DE GIOVANNI FRANCESCO¹,NEWELL MARTIN L.²,RUSSO ALESSIO³

Affiliation:

1. Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, I-80126 Napoli, Italy

2. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

3. Dipartimento di Matematica e Fisica, Seconda Università di Napoli, Viale Lincoln 5, I-81100 Caserta, Italy

Abstract

It is proved that if θ is an endomorphism of a group G such that 〈x, xθ〉 is cyclic for all elements x of G, then θ is a normal endomorphism of G, i.e. it commutes with all inner automorphisms of G.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498813500618

Reference3 articles.

1. Power automorphisms of a group

2. On commuting automorphisms of groups

3. Normal and power endomorphisms of a group

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

4. On cyclic automorphisms of a group;Journal of Algebra and Its Applications;2020-07-04