Total Characters of Dihedral Groups and Sharpness

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...

Group characters, permutation actions and sharpness

We extend the work which has appeared in papers on sharp characters and originated with Blichfeldt and Maillet to the Burnside ring of a finite group G. We show that the polynomial whose zeros are the set of marks of non-identity subgroups on a faithful G-set X evaluated at X is an integral multiple of the regular G-set, and deduce a result about the size of a base of X . Further consequences f...

Generalised Classes in Groups and Association Schemes: Duals of Results on Characters and Sharpness

A result of Strunkov on generalised conjugacy classes of groups is most conveniently expressed in terms of the P-matrix of an association scheme. This result is dual to a result of Blichfeldt on permutation characters, which has been shown by Cameron and Kiyota to hold for arbitrary characters and led to the definition of sharp characters. We show that the result carries over to arbitrary (comm...

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.