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On Groups in Which Many Automorphisms Are Cyclic
- Source :
- Mathematics, Vol 10, Iss 2, p 262 (2022)
- Publication Year :
- 2022
- Publisher :
- MDPI AG, 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.
- Subjects :
- FC-groups
FW-groups
cyclic automorphisms
cyclicizer
Mathematics
QA1-939
Subjects
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 10
- Issue :
- 2
- Database :
- Directory of Open Access Journals
- Journal :
- Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.679a0ea9487448b4ae95823dad23e077
- Document Type :
- article
- Full Text :
- https://doi.org/10.3390/math10020262