The Finite Bruck Loops *
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چکیده
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 P SL2(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.
منابع مشابه
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تاریخ انتشار 2009