Journal Title/Source

Rocky Mountain Journal of Mathematics

Publication Date

2006

Volume

36

Page Numbers

183–212

Document Type

Journal Article

Department

Mathematics and Computer Science

Abstract

In the spirit of Glauberman’s fundamental work in B-loops and Moufang loops [18, 19], 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 [1], and we survey the latter in some detail, especially with regard to the so-called Aschbacher radical.

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