If G is a finite group and N is a normal subgroup of G with two Gconjugacy class sizes of elements of prime power order, then we show that N is nilpotent.

We give an algorithm that decides whether a single equation in group is virtually class $2$ nilpotent with cyclic commutator subgroup, such as the Heisenberg group, admits solution. This generalises work of Duchin, Liang and Shapiro to finite extensions.

We consider several subgroup-related algorithmic questions in groups, modeled after the classic computational lattice problems, and study their computational complexity. We find polynomial time solutions to problems like finding a subgroup element closest to a given group element, or finding a shortest non-trivial element of a subgroup in the case of nilpotent groups, and a large class of surfa...

The concepts of fuzzy semi-ideals of R with respect to H≤R and generalized fuzzy quotient rings are introduced. Some properties of fuzzy semiideals are discussed. Finally, several isomorphism theorems for generalized fuzzy quotient rings are established.

adomian decomposition method has been applied to solve many functional equations so far. in this article, we have used this method to solve the fuzzy differential equation under generalized differentiability. we interpret a fuzzy differential equation by using the strongly generalized differentiability. also one concrete application for ordinary fuzzy differential equation with fuzzy input data...

Recently, Macdonald et. al. showed that many algorithmic problems for finitely generated nilpotent groups including computation of normal forms, the subgroup membership problem, the conjugacy problem, and computation of subgroup presentations can be done in LOGSPACE. Here we follow their approach and show that all these problems are complete for the uniform circuit class TC0 – uniformly for all...

Let m,n be positive integers, v a multilinear commutator word and w = vm. We prove that if G is a residually finite group in which all wvalues are n-Engel, then the verbal subgroup w(G) is locally nilpotent. We also examine the question whether this is true in the case where G is locally graded rather than residually finite. We answer the question affirmatively in the case where m = 1. Moreover...

in this paper, we introduce some properties of an intuitionistic normal fuzzy m-subgroup of m- group with m-homomorphism and isomorphism. we study he image, the pre-image and the inverse mapping of the intuitionistic normal fuzzy m-‎subgroups.‎

In this paper, we introduce some properties of an intuitionistic normal fuzzy m-subgroup of m- group with m-homomorphism and isomorphism. We study he image, the pre-image and the inverse mapping of the intuitionistic normal fuzzy m-‎subgroups.‎

Tree languages recognized by deterministic root-to-frontier recognizers are also called DR-languages. The concept of generalized R-chain languages was introduced by the author in his paper On monotone languages and their characterization by regular expressions (Acta Cybernetica, 18 (2007), 117134.) and it has turned out that the monotone DR-languages are exactly those languages that can be give...