In this paper a rst step in classifying the fuzzy subgroups of a nite nonabelian group is made. We develop a general method to count the number of distinct fuzzy subgroups of such groups. Explicit formulas are obtained in the particular case of dihedral groups.

Abstract. Cyclic sieving is a well-known phenomenon where certain interesting polynomials, especially qanalogues, have useful interpretations related to actions and representations of the cyclic group. We define sieving for an arbitrary group G and study it for the dihedral group I2pnq of order 2n. This requires understanding the generators of the representation ring of the dihedral group. For ...

Let $G$ be a finite group. The reduced power graph of is the undirected whose vertex set $G$, and two distinct vertices $x$ $y$ are adjacent if $\langle x \rangle \subset \langle y \rangle$ or \rangle$. In this paper, we give tight upper lower bounds for metric dimension As applications, compute $\mathcal{P}$-group, cyclic group, dihedral generalized quaternion group odd order.

A free bimodule resolution is constructed for the integral group ring of the dihedral group of order 4m. This resolution is applied for a description, in terms of generators and defining relations, of the Hochschild cohomology algebra of this group ring. Introduction Let K be a commutative ring with unity, let R be an associative K-algebra that is a finitely generated projective K-module, let Λ...

We prove that if a K3 surface X admits Z/5Z as a group of symplectic automorphisms, then it actually admits D5 as a group of symplectic automorphisms. The orthogonal complement to the D5-invariants in the second cohomology group of X is a rank 16 lattice, L. It is known that L does not depend on X: we prove that it is isometric to a lattice recently described by R. L. Griess Jr. and C. H. Lam. ...

the analysis of the 27al and 35cl quadrupole coupling parameters of aluminum methyl chloride dimers were carried out on the basis of the density functional theory (dft). the available experimental values of quarupole coupling constants were compared with their calculated ones. in this investigation, the correlations were made between calculated 27al and 35cl nuclear quadrupole coupling constant...