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...

 Letbe a ring with an endomorphism and an -derivationAntoine studied the structure of the set of nilpotent elements in Armendariz rings and introduced nil-Armendariz rings. In this paper we introduce and investigate the notion of nil--compatible rings. The class of nil--compatible rings are extended through various ring extensions and many classes of nil--compatible rings are constructed. We al...

The Chermak–Delgado lattice of a finite group G is self-dual sublattice the subgroup G. In this paper, we focus on groups whose an elementary abelian p-group. We prove that such are nilpotent class 2. also that, for any p-group E, there exists E.

Suppose K is a local field with finite residue field of characteristic p 6= 2 and K<p(M) is its maximal p-extension such that Gal(K<p(M)/K) has period p M and nilpotent class < p. If charK = 0 we assume that K contains a primitive p -th root of unity. The paper contains an overview of methods and results describing the structure of this Galois group together with its filtration by ramification ...

Let V be a variety of not necessarily associative algebras, and A an inverse limit of nilpotent algebras Ai ∈V, such that some finitely generated subalgebra S ⊆A is dense in A under the inverse limit of the discrete topologies on the Ai. A sufficient condition on V is obtained for all algebra homomorphisms from A to finite-dimensional algebras B to be continuous; in other words, for the kernels...

It is proved that for any prime p a finitely generated nilpotent group is conjugacy separable in the class of finite p-groups if and only if the tor-sion subgroup of it is a finite p-group and the quotient group by the torsion subgroup is abelian. 1. Let K be a class of groups. A group G is called residual K (or K-residual) if for each non-unit element a ∈ G there is a homomorphism ϕ of G onto ...

Introduction. One of the first things we learn in abstract algebra is the notion of a cyclic group. For every positive integer n, we have Zn, the group of integers modulo n. When n is prime, a simple application of Lagrange’s theorem yields that this is the only group of order n. We may ask ourselves: what other positive integers have this property? In this spirit we call a positive integer n a...

The main result of the current paper is a new parametrization of the orbits of a symmetric subgroup K on a partial flag variety P . The parametrization is in terms of certain Spaltenstein varieties, on one hand, and certain nilpotent orbits, on the other. One of our motivations, as explained below, is related to enumerating special unipotent representations of real reductive groups. Another mot...

Fix a prime p, and let A be the polynomial part of the dual Steenrod algebra. The Frobenius map on A induces the Steenrod operation P̃0 on cohomology, and in this paper, we investigate this operation. We point out that if p = 2, then for any element in the cohomology of A, if one applies P̃0 enough times, the resulting element is nilpotent. We conjecture that the same is true at odd primes, and t...

Canonical forms are given for the nilpotent BRS operator δ and the covariant ‘loop space’ derivative Dμ for the p-brane fields for all odd p. The defining characteristic of Dμ is that it is a functional derivative operator which generalizes the ordinary functional derivative and also commutes with δ. Methods of construction for the canonical forms are discussed.