An induction theorem inspired by Brauer's induction theorem for characters of finite groups

Davies, Ryan (2018). An induction theorem inspired by Brauer's induction theorem for characters of finite groups. University of Birmingham. Ph.D.

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Abstract

Brauer's induction theorem states that every irreducible character of a finite group G can be expressed as an integral linear combination of induced characters from elementary subgroups.
The goal of this thesis is to develop our own induction theorem inspired by both Brauer's induction theorem and Global-Local conjectures. Specifically we replace the set of elementary subgroups of G by the set of subgroups of index divisible by the prime power divisors of the given character's degree.
We aim to do this by using a reduction theorem to almost simple and quasisimple groups, using the Classification of Finite Simple Groups to deal with the remaining cases.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

Supervisor(s):