Structure and representations of Q-groups

zbMath0546.20005MaRDI QIDQ798416

Dennis R. Kletzing

Publication date: 1984

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

zbMATH Keywords

Weyl groupsconjugacy classessymmetric groupsSylow 2-subgroupswreath productscharacter tablescomplex representationssemi-direct productsinduction theorempermutation charactersexceptional Weyl groupsirreducible involutionQ-groupsrationally valued characters

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Research exposition (monographs, survey articles) pertaining to group theory (20-02)

Related Items (26)

z-Classes and Rational Conjugacy Classes in Alternating Groups ⋮ The Conjugacy Class Number k(G): A Different Perspective ⋮ Some results on ℚ-groups ⋮ On the arithmetic of the representation ring and elements of finite order in Lie groups ⋮ Rational representations and permutation representations of finite groups. ⋮ Rational groups whose character degree graphs are disconnected ⋮ Finite groups in which no two distinct conjugacy classes have the same order ⋮ On the Artin exponent of some rational groups ⋮ A note on the rationality of Sylow 2-subgroups of rational groups ⋮ Rationality of Wreath Products of Groups ⋮ Sylow 2-subgroups of rational solvable groups. ⋮ Induction theorems for finite groups including a common generalization of two classical theorems ⋮ Abelianization and fixed point properties of units in integral group rings ⋮ Frobenius \(\mathbb Q_1\)-groups. ⋮ A note on the rational non-linear characters of groups ⋮ Metabelian \(\mathbb{Q}_1\)-groups ⋮ A new approach to maturity of molecules by rationality of finite groups ⋮ Rational groups and integer-valued characters of Thompson group \(Th\). ⋮ A note on conjugacy classes of finite groups. ⋮ On the p‐adic Stark conjecture at s=1 and applications ⋮ Sylow 2-subgroups of solvable \(\mathbb{Q}_1\)-groups ⋮ Monolithic characters of real groups ⋮ Global and local properties of finite groups with only finitely many central units in their integral group ring ⋮ Groups whose non-linear irreducible characters are rational valued. ⋮ Finite groups with exactly two conjugacy classes of the same order ⋮ Artin Exponent and CC-Subgroups of Rational Groups

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