s-Smith equivalent representations of dihedral groups

Calculations of Dihedral Groups Using Circular Indexation

‎In this work‎, ‎a regular polygon with $n$ sides is described by a periodic (circular) sequence with period $n$‎. ‎Each element of the sequence represents a vertex of the polygon‎. ‎Each symmetry of the polygon is the rotation of the polygon around the center-point and/or flipping around a symmetry axis‎. ‎Here each symmetry is considered as a system that takes an input circular sequence and g...

Dihedral Groups

Limits of Dihedral Groups

We give a characterization of limits of dihedral groups in the space of finitely generated marked groups. We also describe the topological closure of dihedral groups in the space of marked groups on a fixed number of generators.

Smith Equivalence of Representations for Finite Perfect Groups

Using smooth one-fixed-point actions on spheres and a result due to Bob Oliver on the tangent representations at fixed points for smooth group actions on disks, we obtain a similar result for perfect group actions on spheres. For a finite group G, we compute a certain subgroup IO′(G) of the representation ring RO(G). This allows us to prove that a finite perfect group G has a smooth 2–proper ac...

Sumsets in dihedral groups

Let Dn be the dihedral group of order 2n. For all integers r, s such that 1 ≤ r, s ≤ 2n, we give an explicit upper bound for the minimal size μDn (r, s) = min |A · B| of sumsets (product sets) A · B, where A and B range over all subsets of Dn of cardinality r and s respectively. It is shown by construction that μDn (r, s) is bounded above by the known value of μG (r, s), where G is any abelian ...