The finite Bruck Loops

2009/08/18 by Barbara Baumeister, Alexander Stein, Baumeister, Barbara +1
Mathematics · #20E34 #20N05 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20E34 #msc:20N05

paper · pdf · doi:10.48550/arxiv.0908.2597

15 pages

arxiv created 2010/07/14 · arxiv updated 2010/07/16

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 PSL₂(q), q= 9 or q ≥ 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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