Dissertation/Thesis Abstract

On Finitely Generated Nilpotent Groups and Their Subgroups
by Sandor, Bryan, Ph.D., The University of Alabama, 2017, 47; 10262575
Abstract (Summary)

In this work we investigate nilpotent groups G in which all proper subgroups (or all subgroups of infinite index) have class smaller than the class of G. Our main results are obtained by considering analagous questions for Lie algebras and using the Lazard correspondence and the Mal'cev correspondence. Among other things, for each n ≥ 3, we prove the existence of nilpotent groups of class 2n in which every proper subgroup (or subgroup of infinite index) has class at most n.

Indexing (document details)
Advisor: Evans, Martin
Commitee: Corson, Jon, Dixon, Martyn, Stern, Allen, Trace, Bruce
School: The University of Alabama
Department: Mathematics
School Location: United States -- Alabama
Source: DAI-B 78/11(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Class bound on subgroups, Finitely generated nilpotent groups, Nilpotent groups, Proper subgroups, Subgroups of infinite index
Publication Number: 10262575
ISBN: 978-1-369-88282-7
Copyright © 2020 ProQuest LLC. All rights reserved. Terms and Conditions Privacy Policy Cookie Policy