We give a characterization of Σ-cotorsion modules over valuation domains in terms of descending chain conditions on certain chains of definable subgroups. We prove that pure submodules, direct products and modules elementarily equivalent to a Σ-cotorsion module are again Σ-cotorsion. Moreover, we describe the structure of Σ-cotorsion modules.

This paper is considering the competition between two multi-echelon supply-chains on price and service under balance and imbalance of market power between the chains which are analyzing through Nash and Stackelberg game approach. The problem is categorized as the centralized or decentralized structure of each chain, which means a few different possible scenarios are developing based on the Nash...

we model a real-world case problem as a price competition model between two leader-follower supply chains that each of them consists of one manufacturer and one retailer. t he manufacturer produces partially differentiated products and sells to market through his retailer. the retailer sells the products of manufacturer to market by adding some values to the product and gains margin as a fracti...

In this paper, we treat accounting for the number of fuzzy (normal) subgroups finite groups U6n. order to do this, use natural equivalence relation on set U6n, which has a consistent group theoretical foundation. fact, corresponding classes U6n are closely connected structure lattice and chains terminate in regards, Inclusion-Exclusion principle plays an essential role some situations leads rec...

Abstract Let G be a finite group. $H, K$ subgroups of and $H \backslash / the double coset space. If Q is probability on which constant conjugacy classes ( $Q(s^{-1} t s) = Q(t)$ ), then random walk driven by projects to Markov chain /K$ . This allows analysis lumped using representation theory Examples include coagulation-fragmentation processes natural chains contingency tables. Our main exam...

in this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite hamiltonian group. the coverings with three proper subgroups and the principal series of such a group are also counted. finally, we give a complete description of the lattice of characteristic subgroups of a finite h...

‎Let $G$ be a finite group‎. ‎By $MT(G)=(m_1,cdots,m_k)$ we denote the type of‎ ‎conjugacy classes of maximal subgroups of $G$‎, ‎which implies that $G$ has exactly $k$ conjugacy classes of‎ ‎maximal subgroups and $m_1,ldots,m_k$ are the numbers of conjugates‎ ‎of maximal subgroups of $G$‎, ‎where $m_1leqcdotsleq m_k$‎. ‎In this paper‎, ‎we‎ ‎give some new characterizations of finite groups by ...

We prove that if an ultrafilter L is not coherent to a Q-point, then each analytic non-σ-bounded topological group G admits an increasing chain 〈Gα : α < b(L)〉 of its proper subgroups such that: (i) ⋃ α Gα = G; and (ii) For every σ-bounded subgroup H of G there exists α such that H ⊂ Gα. In case of the group Sym(ω) of all permutations of ω with the topology inherited from ω this improves upon e...

In this paper, Kekule structures of benzenoid chains are considered. It has been shown that the coefficients of a B_n (x) Morgan-Voyce polynomial equal to the number of k-matchings (m(G,k)) of a path graph which has N=2n+1 points. Furtermore, two relations are obtained between regularly zig-zag nonbranched catacondensed benzenid chains and Morgan-Voyce polynomials and between regularly zig-zag ...