A classification of groups satisfying the converse of Lagrange's theorem

This paper is a classification of finite groups satisfying the converse of Lagrange's Theorem. We begin by showing a series of inclusions of classes of finite groups: p-groups {dollar}\subseteq{dollar} nilpotent {dollar}\subseteq{dollar} supersolvable {dollar}\subseteq{dollar} polycyclic {dollar}\subseteq{dollar} solvable. The crucial point of the paper consists of the proof that the class of supersolvable groups is contained in the class of converse Lagrange groups while the class of polycyclic groups is not. We also show that finite cyclic groups and finite abelian groups are included in the class of converse Lagrange groups. Finally, we give an example to show that the class of converse Lagrange groups is not contained in the class of supersolvable groups.

Name thesis:degree_name

Master of Science (MS)

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematical Sciences

Grantor dc:publisher

University of Nevada, Las Vegas

Year

1995

Author dc:creator

• Laurent, Laura Earl

Statement dc:rights

• IN COPYRIGHT. For more information about this rights statement, please visit http://rightsstatements.org/vocab/InC/1.0/

Language dc:language

English

Identifier

https://oasis.library.unlv.edu/rtds/463

OAI identifier oai:identifier

oai:oasis.library.unlv.edu:rtds-1462