CEU Electronic Theses and Dissertations, 2016
| Author | Chimpinde, Trevor Chilombo |
|---|---|
| Title | Maximal Subgroups and Character Theory |
| Summary | In this thesis, we consider two group theoretical problems involving maximal subgroups. The first problem is about the upper bound of the maximal subgroups of a finite solvable group. Newton gave the best well upper bound of the number of maximal subgroups of solvable groups. We follow his ideas but give a slightly different proof of this result. The other problem has to do with the relationship between maximal subgroups and primitive permutation character of solvable groups. These characters are multiplicity-free and any two distinct primitive permutation characters only have the trivial character in common. We will show that if all the irreducible complex characters of a solvable group occur as constituents of primitive permutation characters of the group then the group is either elementary Abelian or is a Frobenius group, whose kernel is elementary Abelian and the complement is a cyclic group of prime order. |
| Supervisor | Hegedus, Pal |
| Department | Mathematics MSc |
| Full text | https://www.etd.ceu.edu/2016/chimpinde_trevor.pdf |
Visit the CEU Library.
© 2007-2021, Central European University