Geodesic
Converse Lagrange theorem orders and supersolvable orders
Journal of integer sequences, Tome 19 (2016) no. 8.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 20F16, 20D20, 20K27, 68R05
Keywords: finite group, converse Lagrange theorem order, supersolvable order 
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     author = {Machale, Des and Manning, Joseph},
     title = {Converse {Lagrange} theorem orders and supersolvable orders},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {19},
     number = {8},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_8_a0/}
}
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Machale, Des; Manning, Joseph. Converse Lagrange theorem orders and supersolvable orders. Journal of integer sequences, Tome 19 (2016) no. 8. http://geodesic.mathdoc.fr/item/JIS_2016__19_8_a0/