Some results on finite-by-supersoluble groups

• Main Authors: Petalcorin, Gaudencio C., Jr., Cossey, John, Nochefranca, Luz
• Format: text
• Published: Animo Repository 2007
• Subjects: Group theory; Finite groups; Algebra; Mathematics; Physical Sciences and Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/faculty_research/13525
• Institution: De La Salle University

A finite-by-supersoluble group is one having a finite normal subgroup in which the corresponding quotient is supersoluble. This paper presents some charatcrization of this class of groups. We will see later that the class of finite-by-supersoluble groups is closed with respect to the formation of subgroups and homomorphic images. We also introduce in this paper the notion of a series defined to be a normal series in which the factors are infinite cyclic or finite. By Schreier's Refinement Theorern, the number of infinite cyclic factors in any series is invariant, we call this invariant as the length. The main results of this paper are the following: 1. A group is finite-by-supersoluble if and only if it has a series. 2. A finite-by-supersoluble group is supersoluble-by-finite.