Finite Groups in Which Pronomality and 𝔉-Pronormality Coincide

Authors

Adolfo Ballester-Bolinches, Universitat de València, Spain
James C. Beidleman, University of KentuckyFollow
Arnold D. Feldman, Franklin and Marshall College
Matthew F. Ragland, Auburn University at Montgomery

Abstract

For a formation 𝔉, a subgroup U of a finite group G is said to be 𝔉-pronormal in G if for each g ∈ G, there exists x ∈ ⟨U, U^g⟩ ^𝔉 such that U^x = U^g. If 𝔉 contains 𝔑, the formation of nilpotent groups, then every 𝔉-pronormal subgroup is pronormal and, in fact, 𝔑-pronormality is just classical pronormality. The main aim of this paper is to study classes of finite soluble groups in which pronormality and 𝔉-pronormality coincide.

Document Type

Article

Publication Date

12-9-2015

Notes/Citation Information

Published in Journal of Group Theory, v. 19, issue 2, p. 323-329.

© de Gruyter 2016

The copyright holder has granted the permission for posting the article here.

Digital Object Identifier (DOI)

https://doi.org/10.1515/jgth-2015-0035

Funding Information

The first author has been supported by the grant MTM2010-19938-C03-01 from MICINN (Spain) and Project of NSFC (11271085).

Repository Citation

Ballester-Bolinches, Adolfo; Beidleman, James C.; Feldman, Arnold D.; and Ragland, Matthew F., "Finite Groups in Which Pronomality and 𝔉-Pronormality Coincide" (2015). Mathematics Faculty Publications. 21.
https://uknowledge.uky.edu/math_facpub/21