On the length of the conjugacy classes of finite groups

DOI10.1016/0021-8693(90)90168-NzbMath0694.20015MaRDI QIDQ909029

David Chillag, Marcel Herzog

Publication date: 1990

Published in: Journal of Algebra (Search for Journal in Brave)

zbMATH Keywords

Sylow subgroupsirreducible complex characterscharacter degreessupersolvable groupsnilpotency classderived lengthlengths of conjugacy classes

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Arithmetic and combinatorial problems involving abstract finite groups (20D60) General structure theorems for groups (20E34) Automorphisms of abstract finite groups (20D45)

Related Items (69)

On conjugacy class sizes of \(\pi\)-elements of primary orders in finite groups. ⋮ Finite groups with small conjugacy classes ⋮ THE INFLUENCE OF CONJUGACY CLASS SIZES ON THE STRUCTURE OF FINITE GROUPS: A SURVEY ⋮ Variations on a theorem by Alan Camina on conjugacy class sizes. ⋮ Remarks on the length of conjugacy classes of finite groups ⋮ Coprime action and arithmetical conditions on invariant conjugacy classes. ⋮ On class numbers of a finite group and of its subgroups ⋮ Notes on the Drinfeld Double of Finite-dimensional Group Algebras ⋮ Conjugacy class lengths of metanilpotent groups ⋮ On the orders of conjugacy classes of cyclic subgroups ⋮ Prime divisors of irreducible character degrees and of conjugacy class sizes in finite groups ⋮ Prime powers as conjugacy class lengths of π-elements ⋮ On character degrees quotients ⋮ Square-free class sizes in products of groups ⋮ PGL2(q) cannot be determined by its cs ⋮ On the conjugacy class lengths of finite groups. ⋮ On an extension of a theorem on conjugacy class sizes. ⋮ Finite groups with exactly two class lengths of elements of prime power order ⋮ Thompson's conjecture for alternating group of degree 22. ⋮ On the normal subgroup with coprime \(G\)-conjugacy class sizes ⋮ Lengths of conjugacy classes of π-elements and primary elements in finite groups ⋮ Groups whose vanishing class sizes are p-powers ⋮ Non-solvable groups all of whose indices are odd-square-free ⋮ GENERALIZING A THEOREM OF HUPPERT AND MANZ ⋮ Finite groups with graphs containing no triangles ⋮ Prime power indices in factorised groups ⋮ \(X\)-decomposable finite groups for \(X=\{1, m,m + 1, m + 2\}\) ⋮ ON SUB-CLASS SIZES OF FINITE GROUPS ⋮ Groups in which the centralizer of any non-central element is maximal ⋮ Influence of conjugacy class sizes of some elements on the structure of a finite group ⋮ Conjugacy class sizes in arithmetic progression ⋮ A new characterization of \(A_{12}\). ⋮ Mutually permutable products and conjugacy classes. ⋮ Groups with some arithmetic conditions on real class sizes. ⋮ Thompson's conjecture for Lie type groups \(E_7(q)\). ⋮ Conjugacy class sizes of elements of prime-power order of finite groups ⋮ Lengths of conjugacy classes of finite solvable groups ⋮ Prime Factors of Conjugacy Classes of Finite Solvable Groups ⋮ ON CONJUGACY CLASS SIZES AND CHARACTER DEGREES OF FINITE GROUPS ⋮ On the normal subgroup with minimal \(G\)-conjugacy class sizes ⋮ The influence of conjugacy class sizes on the structure of finite groups ⋮ Finite groups with three conjugacy class sizes of some elements. ⋮ Certain relations between p-regular class sizes and the p-structure of p-solvable groups ⋮ On finite \(X\)-decomposable groups for \(X=\{1,2,4\}\). ⋮ Notes on the length of conjugacy classes of finite groups. ⋮ Indices of elements and normal structure of finite groups. ⋮ Finite groups with the same conjugacy class sizes as a finite simple group ⋮ Invariant class sizes and solvability of finite groups under coprime action ⋮ On finite groups with square-free conjugacy class sizes ⋮ Character degrees, conjugacy class sizes, and element orders: three primes ⋮ Characterization of simple \(K_4\)-groups. ⋮ On coprime \(G\)-conjugacy class sizes in a normal subgroup. ⋮ On Lengths of Conjugacy Classes and Character Degrees in Finite Groups ⋮ On sub-class sizes of mutually permutable products ⋮ Conjugacy classes in finite groups ⋮ On Conjugacy Class Sizes of the p′-Elements with Prime Power Order ⋮ On Thompson's Conjecture ofA₁₀ ⋮ Applications of a graph related to conjugacy classes in finite groups ⋮ On the set of same-size conjugate classes ⋮ Groups whose vanishing class sizes are prime powers ⋮ Monomiality of finite groups with some conditions on conjugacy classes. ⋮ On the lengths of conjugaey classes ⋮ On the normal subgroup with exactly two \(G\)-conjugacy class sizes. ⋮ Recognizing direct products from their conjugate type vectors ⋮ On the diameter of a graph related to \(p\)-regular conjugacy classes of finite groups ⋮ Non-solvable groups each of whose vanishing class sizes has at most two prime divisors ⋮ Conjugacy class sizes of some elements and solvability of finite groups. ⋮ A note on class sizes of vanishing elements in finite groups ⋮ On \(p\)-regular \(G\)-conjugacy class sizes.

Cites Work

• A note on character degrees of solvable groups
• Lineare auflösbare Gruppen
• Endliche nicht-auflösbare Gruppen, deren sämtliche Charaktergrade Primzahlpotenzen sind
• Degree-problems. I: Squarefree character degrees
• Endliche auflösbare Gruppen, deren sämtliche Charaktergrade Primzahlpotenzen sind. (Finite solvable groups all whose character degrees are prime powers)
• Solvable groups character degrees and sets of primes
• A finite simple group of Lie type has p-blocks with different defects, \(p\neq 2\)
• Blocks of defect zero in finite simple groups of Lie type
• A characterization of groups in terms of the degrees of their characters. II
• Groups as Unions of Proper Subgroups
• Finite Groups with Nilpotent Centralizers
• Degree Problems: the p -Rank in p -Solvable Groups
• [https://portal.mardi4nfdi.de/wiki/Publication:5513801 Groups with Normal, Solvable Hall p � -Subgroups]
• Endliche Gruppen I
• Group Characters and Normal Hall Subgroups
• Some Studies on Group Characters
• On the Degrees of Irreducible Representations of a Finite Group
• Group Elements of Prime Power Index
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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