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On Twisted Subgroups and Bol Loops of Odd Order

Tuval Foguel·Michael K. Kinyon·J. D. Phillips
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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.

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Tuval Foguel, Michael K. Kinyon, J. D. Phillips. 2004-05-04. On Twisted Subgroups and Bol Loops of Odd Order. https://arxiv.org/abs/math/0208231

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