A characteristic condition of finite nilpotent group.

Nilpotent Orbits in Classical Lie Algebras over Finite Fields of Characteristic 2 and the Springer Correspondence

Let G be an adjoint algebraic group of type B, C, or D over an algebraically closed field of characteristic 2. We construct a Springer correspondence for the Lie algebra of G. In particular, for orthogonal Lie algebras in characteristic 2, the structure of component groups of nilpotent centralizers is determined and the number of nilpotent orbits over finite fields is obtained.

Finite groups and Lie rings with a metacyclic Frobenius group of automorphisms

Suppose that a finite group G admits a Frobenius group of automorphisms FH of coprime order with cyclic kernel F and complement H such that the fixed point subgroup CG(H) of the complement is nilpotent of class c. It is proved that G has a nilpotent characteristic subgroup of index bounded in terms of c, |CG(F )|, and |F | whose nilpotency class is bounded in terms of c and |H| only. This gener...

On a conjecture of a bound for the exponent of the Schur multiplier of a finite $p$-group

Let $G$ be a $p$-group of nilpotency class $k$ with finite exponent $exp(G)$ and let $m=lfloorlog_pk floor$. We show that $exp(M^{(c)}(G))$ divides $exp(G)p^{m(k-1)}$, for all $cgeq1$, where $M^{(c)}(G)$ denotes the c-nilpotent multiplier of $G$. This implies that $exp( M(G))$ divides $exp(G)$, for all finite $p$-groups of class at most $p-1$. Moreover, we show that our result is an improvement...

Finite Groups With a Certain Number of Elements Pairwise Generating a Non-Nilpotent Subgroup

On Some of the Residual Properties of Finitely Generated Nilpotent Groups

In recent years, the RFRS condition has been used to analyze virtual fibering in 3-manifold topology. Agol’s work shows that any 3-manifold with zero Euler characteristic satisfying the RFRS condition on its fundamental group virtually fibers over the circle. In this note we will show that a finitely generated nilpotent group is either virtually abelian or is not virtually RFRS. As a corollary,...