title: Some subgroup embeddings in finite groups: A mini review.
abstract: In this survey paper several subgroup embedding properties related to some types of permutability are introduced and studied.
authors.affiliation: Departament d'Àlgebra, Universitat de València, Dr. Moliner, 50, 46100 Burjassot, València, Spain.
authors.forename: A
authors.initials: A
authors.lastname: Ballester-Bolinches
authors.affiliation: Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA.
authors.forename: J C
authors.initials: JC
authors.lastname: Beidleman
authors.affiliation: Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, Camí de Vera, s/n, 46022 València, Spain.
authors.forename: R
authors.initials: R
authors.lastname: Esteban-Romero
authors.affiliation: Department of Mathematics, Auburn University at Montgomery, P.O. Box 244023, Montgomery, AL 36124-4023, USA.
authors.forename: M F
authors.initials: MF
authors.lastname: Ragland
keywords: Finite group; Permutability; Primitive subgroup; Quasipermutable subgroup; S-permutability; Semipermutability