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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].
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 su
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
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
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 w
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 he