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arXiv · 0908.2597

The finite Bruck Loops

Barbara Baumeister·Alexander Stein
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Abstract

We continue the work by Aschbacher, Kinyon and Phillips [AKP] as well as of Glauberman [Glaub1,2] by describing the structure of the finite Bruck loops. We show essentially that a finite Bruck loop $X$ is the direct product of a Bruck loop of odd order with either a soluble Bruck loop of 2-power order or a product of loops related to the groups $PSL_2(q)$, $q= 9$ or $q \geq 5$ a Fermat prime. The latter possibillity does occur as is shown in [Nag1, BS]. As corollaries we obtain versions of Sylow's, Lagrange's and Hall's Theorems for loops.

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Barbara Baumeister, Alexander Stein. 2010-07-14. The finite Bruck Loops. https://arxiv.org/abs/0908.2597

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