The Number of Conjugacy Classes of a Finite Group and its Sylow p-subgroups

Authors

Cong Tuan Son Van, College of Saint Benedict/Saint John's University

Document Type

Thesis

Publication Date

2011

Disciplines

Mathematics | Physical Sciences and Mathematics

Advisor

Bret Benesh, Mathematics

Abstract

The project will investigate the relationship between the number of conjugacy classes of a finite group and the number of conjugacy classes of its Sylow p-subgroups. The idea of this project comes from problem 14.74 of the Kourovka Notebook of Unsolved Problems in Group Theory (submitted by L. Pyber). The problem states: "Let k(H) denote the number of conjugacy classes of a group H, and G be a finite group with Sylow p-subgroups P₁, ... , P_n. Prove or disprove: k(G) ≤ k(P₁) ... k(P_n)". In this project, we will discuss my approach to this problem, some upper bounds of k(G), some lower bounds of k(P_i) and some families of groups for which this result holds.

Recommended Citation

Van, Cong Tuan Son, "The Number of Conjugacy Classes of a Finite Group and its Sylow p-subgroups" (2011). Honors Theses, 1963-2015. 110.
https://digitalcommons.csbsju.edu/honors_theses/110