Toward the Abelian Root Groups Conjecture for Special Moufang Sets
نویسنده
چکیده
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.
منابع مشابه
Special Moufang Sets, Their Root Groups and Their Μ-maps
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...
متن کاملSpecial abelian Moufang sets of finite Morley rank
Moufang sets are split doubly transitive permutation groups, or equivalently, groups with a split BN-pair of rank one. In this paper, we study so-called special Moufang sets with abelian root groups, under the model-theoretic restriction that the groups have finite Morley rank. These groups have a natural base field, and we classify them under the additional assumption that the base field is in...
متن کاملProper 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...
متن کاملFinite Special Moufang Sets of Odd Characteristic
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...
متن کاملNew characterization of some linear groups
There are a few finite groups that are determined up to isomorphism solely by their order, such as $mathbb{Z}_{2}$ or $mathbb{Z}_{15}$. Still other finite groups are determined by their order together with other data, such as the number of elements of each order, the structure of the prime graph, the number of order components, the number of Sylow $p$-subgroups for each prime $p$, etc. In this...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008