We prove that the Scott module whose vertex is isomorphic to a direct product of generalized quaternion $2$-group and cyclic Brauer indecomposable. This result generalizes similar results which are obtained for abelian, dihedral, quaternion, semidihedral wreathed vertices.

We show that a finite dihedral group does not act pseudofreely and locally linearly on an even-dimensional sphere S, with k > 1. This answers a question of R. S. Kulkarni from 1982.

In this paper, first, we briefly describe the dihedral group D4 that serves as the basis for calculating saliency in our proposed model. Second, our saliency model makes two major changes in a latest state-of-the-art model known as group-based asymmetry. First, based on the properties of the dihedral group D4, we simplify the asymmetry calculations associated with the measurement of saliency. T...

If a finite group G acts freely and simplicially on a complex homotopy equivalent to a sphere S, then G has periodic Tate cohomology: H (G;Z) ∼= H (G;Z) for all i > 0. Swan proved in [26] that this condition was also sufficient. For free topological actions on S itself, the first additional restriction is: Theorem. [19] A finite dihedral group does not act freely and topologically on S. Milnor’...

In this paper, we consider the kernel of the natural projection from the Artin group of dihedral type I2(k) to the corresponding Coxeter group, which we call the pure Artin group of dihedral type. We present a rational function expression for the spherical growth series of the pure Artin group of dihedral type with respect to a natural generating set.

The finite dihedral group generated by one rotation and reflection is the simplest case of non-abelian group. Cayley graphs are diagrammatic counterparts groups. In this paper, much attention given to graph Considering characteristics elements in group, we propose a model three-state discrete-time quantum walk (DTQW) on Caylay with Grover coin. We derive analytic expressions for position probab...

We prove that any two continuous minimal (topologically free) actions of the infinite dihedral group on an compact Hausdorff space are continuously orbit equivalent only if they conjugate. also show above fails we replace by certain other virtually cyclic groups, e.g., direct product integer with non-abelian finite simple group.