Geodesic
Converse Lagrange theorem orders and supersolvable orders
Journal of integer sequences, Tome 19 (2016) no. 8
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 
@article{JIS_2016__19_8_a0,
     author = {Machale,  Des and Manning,  Joseph},
     title = {Converse {Lagrange} theorem orders and supersolvable orders},
     journal = {Journal of integer sequences},
     year = {2016},
     volume = {19},
     number = {8},
     zbl = {1359.20012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_8_a0/}
}
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%A Manning,  Joseph
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%J Journal of integer sequences
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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/