Department of Mathematics

## FUSION SYSTEMS SEMINAR

"Schur-Zassenhaus theorem and Hall subgroups"

By

# (Senior Project Presentation)

Abstract: The goal of this talk is to explain some tools for Hall subgroups, including Schur-Zassenhaus Theorem, and introduce Hall subgroups and $\pi$-separable groups in view of these tools. First, a criterion for nilpotence will be discussed. Then a detailed proof of Schur-Zassenhaus Theorem, using group extensions, will be given. After a short introduction of $\pi$-subgroups, Hall subgroups will be introduced to lead to some results on $\pi$-separable and $\pi$-solvable groups. Similarities between the results on Hall subgroups and Sylow theorems will be emphasized. Finally, relations between solvability and $\pi$-separability will be presented.




Date:  Tuesday, MAY 3 2016

Time: 13:40 - 14:30

Place: Mathematics Seminar Room, SA-141

All are cordially invited. Tea and biscuits after the seminar.