Search results for "Character theory"

Character sums and double cosets

2008

Abstract If G is a p-solvable finite group, P is a self-normalizing Sylow p-subgroup of G with derived subgroup P ′ , and Ψ is the sum of all the irreducible characters of G of degree not divisible by p, then we prove that the integer Ψ ( P ′ z P ′ ) is divisible by | P | for all z ∈ G . This answers a question of J. Alperin.

Character correspondences in blocks with normal defect groups

2014

Abstract In this paper we give an extension of the Glauberman correspondence to certain characters of blocks with normal defect groups.

Primitive characters of subgroups ofM-groups

1995

One of the hardest areas in the Character Theory of Solvable Groups continues to be the monomial groups. A finite group is said to be an M-group (or monomial) if all of its irreducible characters are monomial, that is to say, induced from linear characters. Two are still the main problems on M-groups: are Hall subgroups of M groups monomial? Under certain oddness hypothesis, are normal subgroups of M-groups monomial? In both cases there is evidence that this could be the case: the primitive characters of the subgroups in question are the linear characters. This is the best result up to date ([4], [6]). Recently, some idea appears to be taking form. In [14], T. Okuyama proved that if G is an…

2-Brauer correspondent blocks with one simple module

2017

Abstract One of the main problems in representation theory is to understand the exact relationship between Brauer corresponding blocks of finite groups. The case where the local correspondent has a unique simple module seems key. We study this situation for 2-blocks.

Some applications of a fundamental theorem by Gluck and Wolf in the character theory of finite groups

1986

Penal Contextualism and Ideational Frameworks: A Guide for the Perplexed

2017

In my paper, I attempt a critical review of Nicola Lacey’s book In Search of Criminal Responsibility, by arguing, firstly, that she gives the categories of “character responsibility” and “capacity responsibility” an over-inclusive account, which results from her filling each of them with views that are not only disparate but also based, at least in part, on conflicting principles; and, secondly, that Lacey’s spelling out of various conceptions of “criminal responsibility” necessarily entails an underlying unitary definition of its subject matter, that is, the concept of “criminal responsibility,” which seems to conflict with her (version of) penal contextualism.

A character-theory-free characterization of the Mathieu group M12

1990

AbstractThe known characterization of the Mathieu group M12 by the structure of the centralizer of a 2-central involution is based on the application of the theory of exceptional characters and uses in addition a block theoretic result which asserts that a simple group of order |M12| is isomorphic to M12. The details of the proof of the latter result had never been published. We show here that M12 can be handled in a completely elementary and group theoretical way.

Characters and Blocks of Finite Groups

1998

This is a clear, accessible and up-to-date exposition of modular representation theory of finite groups from a character-theoretic viewpoint. After a short review of the necessary background material, the early chapters introduce Brauer characters and blocks and develop their basic properties. The next three chapters study and prove Brauer's first, second and third main theorems in turn. These results are then applied to prove a major application of finite groups, the Glauberman Z*-theorem. Later chapters examine Brauer characters in more detail. The relationship between blocks and normal subgroups is also explored and the modular characters and blocks in p-solvable groups are discussed. Fi…

Something Borrowed : Interfigural Characterisation in Anglo-American Fantasy Comics

2016

It is no secret that comics’ formal structure resembles a pastiche: images, words and gaps of different styles and abstraction levels mix to tell a story that is more than their sum. Is it any wonder, then, that modern, myth-driven graphic novels tend to borrow their content elements – such as characters – from several heterogeneous sources as well? Wolfgang G. Müller's little-known but widely applicable theory of interfigurality (1991) shows how literary characters gain depth and resonance by sharing elements with characters in other works. The chapter revises his theory and shows how it could also be used in the analysis of comic book characters. Fantasy comics from Vertigo series like Fa…

Irreducible characters of $3'$-degree of finite symmetric, general linear and unitary groups

2018

Abstract Let G be a finite symmetric, general linear, or general unitary group defined over a field of characteristic coprime to 3. We construct a canonical correspondence between irreducible characters of degree coprime to 3 of G and those of N G ( P ) , where P is a Sylow 3-subgroup of G . Since our bijections commute with the action of the absolute Galois group over the rationals, we conclude that fields of values of character correspondents are the same.