Restriction and induction for supercharacters of finite groups of triangular type

TL;DR

This paper explores the properties of supercharacters in finite groups of triangular type, demonstrating how restrictions decompose into supercharacters and establishing a superinduction framework with a Frobenius-like formula.

Contribution

It introduces the concept of superinduction and proves a Frobenius formula analog for supercharacters in finite groups of triangular type.

Findings

Restriction of supercharacters decomposes into a sum of supercharacters with nonnegative integer coefficients.

Superinduction is defined and an analog of the Frobenius formula is established.

Provides new tools for analyzing supercharacters in triangular type groups.

Abstract

It is proved the the restriction of any supercharacter of a finite group of triangular type on its subgroup is a sum of supercharacters with nonnegative integer coefficients. We define superinduction and prove the analog of the Frobenius formula for supercharacters.