Converse Lagrange theorem orders and supersolvable orders

MacHale, Desmond; Manning, Joseph

Converse Lagrange theorem orders and supersolvable orders

Files

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Published version

Date

2016

Authors

MacHale, Desmond

Manning, Joseph

Publisher

University of Waterloo

Abstract

For finite groups, we investigate both converse Lagrange theorem (CLT) orders and supersolvable (SS) orders, and see that the latter form a proper subset of the former. We focus on the difference between these two sets of orders, reformulate the work of earlier authors algorithmically, and construct a computer program to enumerate such NSS-CLT orders. We establish several results relating to NSS and CLT orders and, working from our computer-generated data, propose a pair of conjectures and obtain a complete characterization of the most common form of NSS-CLT order.

Keywords

Supersolvable (SS) orders , Lagrange theorem (CLT

Citation

MacHale, D. and Manning, J. (2016) 'Converse Lagrange theorem orders and supersolvable rders', Journal of Integer Sequences, 19 (8), 16.8.7, (11 pp).