R. S. Kulkarni showed that a finite group acting pseudofreely, but not freely, preserving orientation, on an even-dimensional sphere (or suitable sphere-like space) is either a periodic group acting semifreely with two fixed points, a dihedral group acting with three singular orbits, or one of the polyhedral groups, occurring only in dimension 2. It is shown here that the dihedral group does no...

We prove that if a K3 surface X admits Z/5Z as group of symplectic automorphisms, then it actually admits D5 as 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. We a...

Let p be an odd prime and Λ=Z[D2p] the integral group ring of dihedral D2p order 2p. The syzygies Ωr(Z) are stable classes intermediate modules in a free Λ-resolution trivial module. We will discuss explicitly interaction under − ⊗Z−.

This paper, deals with some equivalence relations in fuzzy subgroups. Further the probability of commuting two fuzzy subgroups of some finite abelian groups is defined.

One of the concepts in mathematics that developing rapidly today is Graph Theory. The development Theory has been combined with Group Theory, by representing a group graph. intersection graph from , noted whose vertices are all non-trivial subgroups and two distinct adjacent if only . In this research Dihedral group, we looking for shapes numerical invariants. results obtained then subgraphs gi...