Converse Lagrange theorem orders and supersolvable orders
University of Waterloo
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.
Supersolvable (SS) orders , Lagrange theorem (CLT
MacHale, D. and Manning, J. (2016) 'Converse Lagrange theorem orders and supersolvable rders', Journal of Integer Sequences, 19 (8), 16.8.7, (11 pp).
© The Authors 2016.