The integral representation algebra A(RG) is C ®z a(RG). When does a(RG) contain nontrivial nilpotent elements? Let | G\ = pn, where p\n, p prime. Denote by Zp the £-adic valuation ring in Q, and by Zp* its completion. Reiner has shown (i) If a = l , then A(ZPG) and A(Z*G) have no nonzero nilpotent elements (see [ l ] ) . (ii) If ce^2, and G has an element of order p, then both A(ZPG) and A{Z*G...

In this paper we address the problem of understanding when a verbal subgroup finite group is p -nilpotent, with prime, that is, all its elements ′ -order determine subgroup. We provide two -nilpotency criteria, one for terms lower central series any and derived soluble group, which relies on arithmetic properties related to order products commutators .

The purpose of this paper is to describe structural properties of automata whose transition semigroups have a zero, left zero, right zero or bi-zero, or are nilpotent extensions of rectangular bands, left zero bands or right zero bands, or are nilpotent. To describe the structure of these automata we use various well-known decomposition methods of automata theory – direct sum decompositions, su...

fuzzy logic, 67algebraic semantics, 53approximate reasoning, 6axiomatic extensions of MTL, 56 Bellman, R., 21bipolar possibilistic logic, 93BL logic, 51 canonical chain, 66canonical completeness, 66canonical extension, 83Carnap, R., 3comparative truth, 63compositionality, 29computational complexity, 73core fuzzy logic, 58 De Finetti B., 3degre...

In a recent article [Gi99], V.Ginzburg introduced and studied in depth the notion of a principal nilpotent pair in a semisimple Lie algebra g. He also obtained several results for more general pairs. As a next step, we considered in [Pa99] almost principal nilpotent pairs. The aim of this paper is to make a contribution to the general theory of nilpotent pairs. Roughly speaking, a nilpotent pai...

We shall term a group G supersoluble if every homomorphic image H9*l of G contains a cyclic normal subgroup different from 1. Supersoluble groups with maximum condition, in particular finite supersoluble groups, have been investigated by various authors: Hirsch, Ore, Zappa and more recently Huppert and Wielandt. In the present note we want to establish the close connection between supersoluble ...

generalizing the concepts of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and   -fuzzy bi (generalized bi-) ideals in ternary semigroups, the notions of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and -fuzzy bi (generalized bi-) in ternary semigroups are introduced and several related properties are investigated. some new results are obtained.

We prove that a torsion group G with all subgroups subnormal is a nilpotent group or G = N(A1×· · ·×An) is a product of a normal nilpotent subgroup N and pi -subgroups Ai , where Ai = A (i) 1 · · ·A (i) mi G , A (i) j is a Heineken–Mohamed type group, and p1, . . . , pn are pairwise distinct primes (n ≥ 1; i = 1, . . . , n; j = 1, . . . ,mi and mi are positive integers).

A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that [F, h] = F for all nonidentity elements h ∈ H. Suppose that a finite group G admits a Frobenius-like group of automorphisms FH of coprime order with [F ′, H] = 1. In case where CG(F ) = 1 we prove that the groups G and CG(H) have the same nilpotent length un...