We show that every finitely generated nilpotent group of class 2 occurs as the quotient of a finitely presented abelian-by-nilpotent group by its largest nilpotent normal subgroup.

In the variety of all groups, A. I. Mal’cev [5] proved in 1949 that the free product of two residually torsion-free nilpotent groups is again residually torsion-free nilpotent. This paper is motivated by the analogous question in the variety of metabelian groups: can we determine whether free metabelian products of residually torsion-free nilpotent metabelian groups are residually torsion-free ...

A Schmidt group is a non-nilpotent finite group in which each proper subgroup is nilpotent. Each Schmidt group G can be described by three parameters p, q and v, where p and q are different primes and v is a natural number, v ≥ 1. Denote by S the class of all Schmidt groups which have the same parameters p, q and v. It is shown in this paper that the class S can be characterized by the properti...

For the unitary representation of O(p; q) attached to the minimal nilpotent coadjoint orbit, we explicitly calculate its restriction to certain natural dual pairs in O(p; q). We furthermore show how the results are compatible with the orbit method, in particular when viewing the minimal nilpotent orbit as belonging to the limit set of semisimple orbits. R esum e Pour la repr esentation unitaire...

We compute the numbers g(n, 2, 2) of nilpotent groups of order n, of class at most 2 generated by at most 2 generators, by giving an explicit formula for the Dirichlet generating function P

We consider an open problem on the stability of nonlinear nilpotent switched systems posed by Daniel Liberzon. Partial solutions to this problem were obtained as corollaries of global nice reachability results for nilpotent control systems. The global structure is crucial in establishing stability. We show that nice reachability analysis may be reduced to the reachability analysis of a specific...

We study complex product structures on nilpotent Lie algebras, establishing some of their main properties, and then we restrict ourselves to 6 dimensions, obtaining the classification of 6-dimensional nilpotent Lie algebras admitting such structures. We prove that any complex structure which forms part of a complex product structure on a 6-dimensional nilpotent Lie algebra must be nilpotent in ...

Some properties and characterizations for nilpotent matrices are established and in particular, a necessary and sufficient condition for an n × n nilpotent matrix to have the nilpotent index 2 and 3 is given. Mathematics Subject Classification: 15A33; 06D99

We compare orbits in the nilpotent cone of type Bn, that of type Cn, and Kato’s exotic nilpotent cone. We prove that the number of Fq-points in each nilpotent orbit of type Bn or Cn equals that in a corresponding union of orbits, called a type-B or type-C piece, in the exotic nilpotent cone. This is a finer version of Lusztig’s result that corresponding special pieces in types Bn and Cn have th...

We determine the torsion subgroup of the group of endotrivial modules for a finite solvable group in characteristic p. We also prove that our result would hold for p-solvable groups, provided a conjecture can be proved about the case of p-nilpotent groups.