Do you want to publish a course? Click here

Levi decomposition of nilpotent centralisers in classical groups

91   0   0.0 ( 0 )
 Added by David Stewart
 Publication date 2016
  fields
and research's language is English




Ask ChatGPT about the research

We check that the connected centralisers of nilpotent elements in the orthogonal and symplectic groups have Levi decompositions in even characteristic. This provides a justification for the identification of the isomorphism classes of the reductive quotients as stated in [Liebeck, Seitz; Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras].



rate research

Read More

The description of nilpotent Chernikov $p$-groups with elementary tops is reduced to the study of tuples of skew-symmetric bilinear forms over the residue field $mathbb{F}_p$. If $p e2$ and the bottom of the group only consists of $2$ quasi-cyclic summands, a complete classification is given. We use the technique of quivers with relations.
Full residual finiteness growth of a finitely generated group $G$ measures how efficiently word metric $n$-balls of $G$ inject into finite quotients of $G$. We initiate a study of this growth over the class of nilpotent groups. When the last term of the lower central series of $G$ has finite index in the center of $G$ we show that the growth is precisely $n^b$, where $b$ is the product of the nilpotency class and dimension of $G$. In the general case, we give a method for finding an upper bound of the form $n^b$ where $b$ is a natural number determined by what we call a terraced filtration of $G$. Finally, we characterize nilpotent groups for which the word growth and full residual finiteness growth coincide.
Let $sigma ={sigma_{i} | iin I}$ be a partition of the set $Bbb{P}$ of all primes and $G$ a finite group. A chief factor $H/K$ of $G$ is said to be $sigma$-central if the semidirect product $(H/K)rtimes (G/C_{G}(H/K))$ is a $sigma_{i}$-group for some $i=i(H/K)$. $G$ is called $sigma$-nilpotent if every chief factor of $G$ is $sigma$-central. We say that $G$ is semi-${sigma}$-nilpotent (respectively weakly semi-${sigma}$-nilpotent) if the normalizer $N_{G}(A)$ of every non-normal (respectively every non-subnormal) $sigma$-nilpotent subgroup $A$ of $G$ is $sigma$-nilpotent. In this paper we determine the structure of finite semi-${sigma}$-nilpotent and weakly semi-${sigma}$-nilpotent groups.
We study an impartial game introduced by Anderson and Harary. The game is played by two players who alternately choose previously-unselected elements of a finite group. The first player who builds a generating set from the jointly-selected elements wins. We determine the nim-numbers of this game for finite groups of the form $T times H$, where $T$ is a $2$-group and $H$ is a group of odd order. This includes all nilpotent and hence abelian groups.
The authors have shown previously that every locally pro-p contraction group decomposes into the direct product of a p-adic analytic factor and a torsion factor. It has long been known that p-adic analytic contraction groups are nilpotent. We show here that the torsion factor is nilpotent too, and hence that every locally pro-p contraction group is nilpotent.
comments
Fetching comments Fetching comments
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا