Characters of Finite Groups. Volume 2

Name: Characters of Finite Groups. Volume 2 | Volume 2
Brand: De Gruyter
Price: 164.95 EUR
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Volume 2

Yakov G. Berkovich Lev S. Kazarin Emmanuel M. Zhmud'(Autor*in)

De Gruyter (Verlag)

1. Auflage

Erschienen am 17. Dezember 2018

XXII, 703 Seiten

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978-3-11-022409-2 (ISBN)

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Inhalt

Intro
List of frequently met concepts and notations
Preface
XII Finite groups possessing a faithful nonlinear irreducible character with three classes of algebraically conjugate values
1 The first main theorem
2 A 4-values analog to Theorem 1.2
3 The second main theorem
XIII Degrees of irreducible characters of Suzuki $p$-groups
1 Case $p=2$
2 Case $p&2$
XIV Degrees and kernels of irreducible characters
1 Garrison's theorems
2 Theorems of Blichfeldt and Isaacs-Passman
3 Thompson's theorem on degrees
4 Groups with small degrees of irreducible characters
5 A variant of Thompson's Theorem 3.3 (a)
6 Gallagher's theorem
7 Isaacs' three character degrees theorem
8 On intersections of kernels of some characters
9 The Chillag-Herzog theorem
10 Isaacs' theorem
11 Irreducible constituents of faithful induced characters
12 On groups close to Frobenius groups
13 A nilpotency criterion
14 Minkowski's theorem
15 A $\pi$-closure criterion
16 Generalizations of M-groups
17 On Taketa's theorem
18 On Isaacs' solvability criterion
A On Thompson's theorem
XV On monolithic characters
1 Introduction
2 Proof of the main theorem
3 Sagirov's theorems
4 Generalizations of Thompson's and Michler's theorems
5 On Isaacs' three character degrees theorem
6 Some remarks on monolithic characters
A On Zsigmondy primes
XVI Involutions
1 Groups of even order contain a large subgroup
2 Groups with two non-conjugate involutions
3 Real elements
4 Applications to characters
5 Bender's method
6 Brauer's and Thompson's formulas
7 Large subgroups
XVII On disconnected groups
1 The lattice of closed subgroups of a disconnected group
2 Double Frobenius groups and solvable disconnected groups
3 Veitsblit's theorem
4 Proof of Theorem 3.1
5 On Thompson's question
6 Suzuki's theorems on ZT-groups
7 Characterization of Zassenhaus groups
XVIII Linear groups
1 Linear groups of small degree
2 Jordan's theorem
XIX Permutation characters
1 The number of orbits
2 The character of the direct product of two actions
3 Bell numbers and powers of the natural character
4 On characters of $m$-transitive permutation groups
5 Burnside's theorem on transitive groups of prime degree
6 On 4-transitive permutation groups
7 The character table of the symmetric group $\mathrm{S}_5$
8 The character table of the symmetric group $\mathrm{S}_6$
9 The minimal degree of a faithful character of the symmetric group $\mathrm{S}_n$
10 Introduction to Young theory
XX S-characters
1 Definitions and basic properties of S-characters
2 S-characters of the first kind
3 S-characters of the second kind
4 The extremal part of an S-character
5 On systems of S-characters
6 ST-triples
XXI Zeros of characters
1 General facts
2 On the number of zeros of an irreducible character
3 Groups with $\chi$-maximal subgroup
4 Irreducible character with conjugate zeros
5 On zeros of nonlinear irreducible characters
6 Restriction of characters and their zeros
7 Groups with few zeros of a nonlinear character
XXII Metabelian TU-groups with trivial center
1 General facts. Statements of main results
2 Homogeneous metabelian TU-groups
3 Proof of main Theorem 1.12
XXIII The Schur index
XXIV Monolithic character degrees
1 Introduction
2 Solvability
3 Distinct orbit sizes
4 Distinct degrees over an invariant character
5 Groups with distinct nonlinear character degrees
6 Bounding the length
7 Normal Sylow subgroups
8 Sylow derived subgroups
9 Odd commutator factors
10 Transitive Frobenius complements
11 Proof of Theorem C
12 Some examples
XXV Saksonov's theorems on character rings of finite groups
1 On isomorphisms of character rings
2 Units of finite order in character rings
3 Behavior of the regular character under isomorphisms
XXVI Simply reducible groups
1 Wigner's theory
2 Some estimates
3 Solvability of SR-groups
4 Some related results
5 Gelfand pairs and table algebras
XXVII Modular characters
1 Algebraic closure of the Galois field $\mathrm{GF}(p)=\mathbb{F}_p$
2 Brauer characters
3 The Cartan matrix of a group
4 $p$-blocks
5 The orthogonality relations
6 The defect of a $p$-block
7 Blocks of defect 0
8 The defect classes of a $p$-block
9 Defect groups of $G$-classes and $p$-blocks
10 Brauer correspondence. Brauer's first main theorem
11 Brauer's second main theorem
12 Principal $p$-block. Brauer's third main theorem
13 Some applications
Research problems and themes
Bibliography
Author index
Subject index

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