A theorem by Zacher and Rips states that the finiteness of the index of a subgroup can be described in terms of purely lattice-theoretic concepts. On the other hand, it is clear that if G is a group and H is a subgroup of finite index of G, the index |G : H| cannot be recognized in the lattice L(G) of all subgroups of G, as for instance all groups of prime order have isomorphic subgroup lattice...

The aim of this paper is to give some connections between the structure of an abelian finite group and the structure of its subgroup lattice. Let (G, +) be an abelian group. Then the set L(G) of subgroups of G is a modular and complete lattice. Moreover, we suppose that G is finite of order n. If L n is the divisors lattice of n, then the following function is well defined: ord : L(G) −→ L n , ...

Inthispaper, (L,M)-fuzzy domain finiteness and (L,M)-fuzzy restricted hull spaces are introduced, and several characterizations of the category (L,M)-CS of (L,M)-fuzzy convex spaces are obtained. Then, (L,M)-fuzzy stratified (resp. weakly induced, induced) convex spaces are introduced. It is proved that both categories, the category (L,M)-SCS of (L,M)-fuzzy stratified convex spaces and the cate...

This note announces that a simple approximation property, known to hold in large classes of partially ordered locally convex spaces whose duals are lattice ordered (e.g., [Banach or] Fréchet spaces with closed, normal, generating positive cones possessing the Riesz decomposition property), actually characterizes spaces with lattice-ordered duals. Some very mild and natural assumptions about the...

Abstract Given a finite group G , we denote by $L(G)$ the subgroup lattice of and ${\cal CD}(G)$ Chermak–Delgado . In this note, determine groups such that $|{\cal CD}(G)|=|L(G)|-k$ for $k=1,2$

In this paper,  fuzzy convergence theory in the framework of $L$-convex spaces is introduced. Firstly, the concept of $L$-convex remote-neighborhood spaces is introduced and it is shown that the  resulting category is isomorphic to that of $L$-convex spaces. Secondly, by means of $L$-convex ideals, the notion of $L$-convergence spaces is introduced and it is proved that the  category of $L$-con...

This is a survey of algorithmic results in the theory of “discrete convex analysis” for integer-valued functions defined on integer lattice points. The theory parallels the ordinary convex analysis, covering discrete analogues of the fundamental concepts such as conjugacy, the Fenchel min-max duality, and separation theorems. The technical development is based on matroid-theoretic concepts, in ...

In the classical model of cooperative games it is generally assumed that there are no restrictions on cooperation and hence, every subset of players is a feasible coalition. However, in many social and economic situations, this model does not apply. Examples are provided by local public goods which are supplied by local communities, social and sports clubs, labor unions, political parties, and ...

Abel Stolz and Andreas Thom [Proc. Lond. Math. Soc. 108 (2014), pp. 73–102] stated that the lattice of normal subgroups an ultraproduct finite simple groups is always linearly ordered. This false in this form most cases for classical Lie type. We correct statement case point out a version \enquote*relative bounded generation quasisimple its implications on structure such groups.