Undergraduate Honors Theses

Thesis Defended

Spring 2019

Document Type

Thesis

Type of Thesis

Departmental Honors

Department

Mathematics

First Advisor

Dr. Nathaniel Thiem

Second Advisor

Dr. Richard Green

Third Advisor

Dr. Lauries Gries

Abstract

This study focuses on the partitions of a group that arise from: action by conjugation, a two sided multiplicative generalization of conjugation, and inclusion of a subgroup into the group. Since conjugacy classes correspond to irreducible characters, studying the partitions in a group compatible with conjugacy classes in the subgroup, and by analogy, studying the partition of a group compatible with superclasses in a subgroup, invariances in the group can be derived from the subgroup's simpler structure. The fusion of conjugacy classes, and superclasses, has some effects on the calculation of an induced and superinduced function. However, these effects do not change the partition of a group which arises from inducing a class function to it. Understanding why gives a clue to a crucial invariance in the induction process, and this means that induction behaves more like superinduction, which always gives rise to supercharacter theories. So this work aims at furthering Marberg and Thiem's work in Superinduction for Pattern Groups, by presenting some conditions for induction and superinduction to be indentical. In those cases, induced class functions give rise to nontrivial supercharacter theories, which as the title suggests, is the goal.

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