FINITE ZASSENHAUS MOUFANG SETS WITH ROOT GROUPS OF EVEN ORDER
نویسندگان
چکیده
منابع مشابه
Proper Moufang Sets with Abelian Root Groups Are Special
Moufang sets are the Moufang buildings of rank one. They were introduced by J. Tits [T1] as a tool for studying algebraic groups of relative rank one. They are essentially equivalent to split BN -pairs of rank one, and as such they have been studied extensively. In some sense they are the basic ‘building blocks’ of all split BN -pairs. In the finite case, it had been a major project to classify...
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We prove Timmesfeld’s conjecture that special abstract rank one groups are quasisimple. We show that in a special Moufang set the root groups are characterized on the one hand by being regular and normal in the point stabilizer, and on the other hand a normal transitive nilpotent subgroup of the point stabilizer is a root group. We prove that if a root group of a special Moufang set contains an...
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We prove that if a root group of a special Moufang set contains an element of order p ≡ 1 (mod 4) then it is abelian.
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For a finite group $G$, let $Cent(G)$ denote the set of centralizers of single elements of $G$. In this note we prove that if $|G|leq frac{3}{2}|Cent(G)|$ and $G$ is 2-nilpotent, then $Gcong S_3, D_{10}$ or $S_3times S_3$. This result gives a partial and positive answer to a conjecture raised by A. R. Ashrafi [On finite groups with a given number of centralizers, Algebra Collo...
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In this paper we classify finite special Moufang sets M(U, τ ) of odd characteristic. The characteristic 2 case was handled in another paper by De Medts and the author. We prove, using elementary means that U is elementary abelian. Then we show that M(U, τ ) is the unique Moufang set whose little projective group is PSL2(|U |). The emphasis of this paper is on obtaining elementary proofs. Secti...
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ژورنال
عنوان ژورنال: Communications in Contemporary Mathematics
سال: 2011
ISSN: 0219-1997,1793-6683
DOI: 10.1142/s0219199711004506