Search

In this manuscript, we show that at least three weak solutions exist for a non-local $ p(x) $ p (x) -biharmonic problem. The variational method and the critical theorem of Bonanno and Marano (Appl. Anal. 89 (2010), 1–10) are used to prove our main result. [ABSTRACT FROM AUTHOR]

Let G be a finite group. A subgroup of G is called S-quasinormal in G if it permutes with each Sylow subgroup of G. In this paper, we investigate the structure of the finite group G when certain abelian subgroups of largest possible exponent of prime power orders are S-quasinormal in G. [ABSTRACT FROM AUTHOR]

Kaplansky's famous conjectures about generalizing results from groups to Hopf algebras inspired many mathematicians to try to find solusions for them. Recently, Cohen and Westreich in [8] and [10] have generalized the concepts of nilpotency and solvability of groups to Hopf algebras under certain conditions and proved interesting results. In this article, we follow their work and give a detailed example by considering a finite group G and an algebraically closed field K. In more details, we construct the group Hopf algebra H = KG and examine its properties to see what of the properties of the original finite group can be carried out in the case of H. [ABSTRACT FROM AUTHOR]

Let G be a finite group. A subgroup H of G is said to be weakly S-permutable in G if G has a subnormal subgroup T such that G = HT and T ∩ H ≤ HsG, where HsG is the subgroup of H generated by all those subgroups of H which are S-permutable in G. In this paper, we prove the following: For a Sylow p-subgroup P of G (p > 2), suppose that P has a subgroup D such that 1 < |D| < |P| holds and all subgroups H of P with |H| = |D| are weakly S-permutable in G. Then, the commutator subgroup G′ is p-nilpotent. We certainly believe that this result will improve and extend a current and classical theories in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some properties of weak graded rings that are rings graded by a set G of coset representatives for the left action of a subgroup H on a group X. Moreover, a graded rings by using the product H × G are also discussed. A detailed example is given. [ABSTRACT FROM AUTHOR]

In this paper, a new q-analogue of modified Bessel function and its corresponding gen-erating function are given. Also, we used the generating function method to deduce its q--difference equation which gives us the differential equation of the ordinary modified Bessel function when q → 1 and we deduced its recurrence relation. Finally, we established the relation between the two-dimensional quantum algebra Eq(2) and the new q--analogue of modified Bessel function using the realization of the standard Euclidean algebra in one real variable and q--exponentials. [ABSTRACT FROM AUTHOR]

The purpose of this article is to provide mathematical formulas for some operations on the objects of a non-trivially associated tensor category constructed from a factorization of a group into a subgroup and a set of left coset representatives. A detailed example is provided. [ABSTRACT FROM AUTHOR]