Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The finite Bruck Loops   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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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: nlin