Alexander Stein
On Bruck Loops of 2-power Exponent, II.
Thu, 08/20/2009 - 23:06 — SomNambulAuthors: Alexander Stein
Subjects: Group Theory
AbstractAs anounced in [BSS], we show that the non-passive finite simple groups are
among the $PSL_2(q)$ with $q-1 \ge 4$ a 2-power.[BSS]: Baumeister,Stein,Stroth: On Bruck Loops of 2-power Exponent
Commuting graphs of odd prime order elements in simple groups.
Wed, 08/19/2009 - 19:30 — SomNambulAuthors: Barbara Baumeister, Alexander Stein
Subjects: Group Theory
AbstractWe study the commuting graph on elements of odd prime order in finite simple
groups. The results are used in a forthcoming paper describing the structure of
Bruck loops and Bol loops of exponent 2.On Bruck Loops of 2-power Exponent.
Wed, 08/19/2009 - 19:30 — SomNambulAuthors: Barbara Baumeister, Alexander Stein, Gernot Stroth
Subjects: Group Theory
AbstractWe classify "nice" loop envelopes to Bruck loops of 2-power exponent under
the assumption that every nonabelian simple section of $G$ is either passive or
isomorphic to $\PSL_2(q)$, $q-1 \ge 4$ a 2-power. The hypothesis is verified in
a separate paper. This paper is a continuation of the work by Aschbacher,
Kinyon and Phillips on finite Bruck loops [AKP]. In [BS3] we applied these
results and get a neat description of the structure of the finite Bruck loops.The finite Bruck Loops.
Wed, 08/19/2009 - 19:30 — SomNambulAuthors: Barbara Baumeister, Alexander Stein
Subjects: Group Theory
AbstractWe 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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