Let G be a group and D be a subgroup of G. In this paper we are interested in the description of the lattice L(D; G) = fH j D H Gg of subgroups of G which contain D. We call subgroups H 2 L(D; G) subgroups intermediate between D and G. We are primarily interested in the parametrization of intermediate subgroups and their behaviour with respect to set-theoretic and group-theoretic operations lik...

in this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring r. these fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set ...

in this paper, our purpose is twofold. firstly, the tensor andresiduum operations on $l-$nested systems are introduced under thecondition of complete residuated lattice. then we show that$l-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. thus the new representation theorem of$l-$subsets on complete re...

We describe a criterion for real or complex hyperbolic lattice to admit residually finite rational solvable (RFRS) tower that consists entirely of congruence subgroups. use this show certain Bianchi groups PSL 2 (

Introduction In the theory of groups, the important concepts of Abelian group, solvable group, nilpotent group, the center of a group and centraliz-ers, are all defined from the binary operation [x, y] = x −1 y −1 xy. Each of these notions, except centralizers of elements, may also be defined in terms of the commutator of normal subgroups. The commutator [M, N] (where M and N are normal subgrou...

We discuss the topic of full transitivity cotorsion hull a separable p-group. This plays significant role in description lattice fully invariant subgroups group. A condition is established, fulfillment which makes not transitive.

For each integer n ≥ 3 n \geq 3 , we exhibit a n...