On Twisted Subgroups and Bol Loops of Odd Order
Group Theory
2008-01-15 v2
Abstract
In the spirit of Glauberman's fundamental work in B-loops and Moufang loops, we prove Cauchy and strong Lagrange theorems for Bol loops of odd order. We also establish necessary conditions for the existence of a simple Bol loop of odd order, conditions which should be useful in the development of a Feit-Thompson theorem for Bol loops. Bol loops are closely related to Aschbacher's twisted subgroups, and we survey the latter in some detail, especially with regard to the so-called Aschbacher radical.
Cite
@article{arxiv.math/0208231,
title = {On Twisted Subgroups and Bol Loops of Odd Order},
author = {Tuval Foguel and Michael K. Kinyon and J. D. Phillips},
journal= {arXiv preprint arXiv:math/0208231},
year = {2008}
}
Comments
20 pages, AMS-LaTeX, to appear in Rocky Mountain Math. J. Version 2 corrects some serious mistakes, and includes many cosmetic changes suggested by the referee