On Twisted Subgroups and Bol Loops of Odd Order

Details On Twisted Subgroups and Bol Loops of Odd Order On Twisted Subgroups and Bol Loops of Odd Order

2002-08-29

arxiv.org/abs/math/0208231v2

Rocky Mountain J. Math 36 (2006), 183-212.

Mathematics

Group Theory

20 pages, AMS-LaTeX, to appear in Rocky Mountain Math. J. Version 2 corrects some serious mistakes, and includes many cosmetic

Scientific paper

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.

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