Supercharacter theories of dihedral groups

Abstract

The set of supercharacter theories of a fixed group $G$ forms a natural lattice. An open question in the study of supercharacter theories is to classify this lattice, and to date, this has only been done for the cyclic groups ${\mathbb{Z}}_n$. In this paper, we classify the supercharacter theory lattice of the dihedral groups $D_{2n}$ in terms of their cyclic subgroups of rotations.

References in corpus (1)

• The Hopf monoid on nonnesting supercharacters of pattern groups

Cited by in corpus (1)

• Toward a Classification of the Supercharacter Theories of $C_p\times C_p$