Every coprime linear group admits a base of size two

DOI10.1090/tran/6544zbMath1382.20012arXiv1212.0199OpenAlexW3103155265MaRDI QIDQ2790717

Károly Podoski, Zoltán Halasi

Publication date: 8 March 2016

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.0199

zbMATH Keywords

base sizeregular partitioncoprime linear group

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Representation theory for linear algebraic groups (20G05) Modular representations and characters (20C20) Primitive groups (20B15)

Related Items (23)

A proof of Pyber's base size conjecture ⋮ Permutation groups with restricted stabilizers ⋮ Bases of twisted wreath products ⋮ Large \(p'\)-orbits for \(p\)-nilpotent linear groups ⋮ Blocks of small defect in alternating groups and squares of Brauer character degrees ⋮ REGULAR ORBITS OF COPRIME LINEAR GROUPS IN LARGE CHARACTERISTIC ⋮ Problems on characters: solvable groups ⋮ A note on larger orbit size ⋮ IBIS soluble linear groups ⋮ Base sizes of primitive groups of diagonal type ⋮ A lower bound for the number of conjugacy classes of a finite group. ⋮ On the Brauer-Feit bound for abelian defect groups. ⋮ Base sizes for primitive groups with soluble stabilisers ⋮ On blocks with abelian defect groups of small rank ⋮ Upper bounds for the number of irreducible character degrees of a group. ⋮ On base sizes for algebraic groups ⋮ Cartan matrices and Brauer's \(k(B)\)-conjecture. III. ⋮ Random bases for coprime linear groups ⋮ Generalized bases of finite groups ⋮ The minimal base size for a 𝑝-solvable linear group ⋮ Orbit sizes and odd order composition factors of finite linear groups ⋮ Maximal intersections in finite groups ⋮ On Pyber’s base size conjecture

Uses Software

• GAP

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The base size of a primitive diagonal group.
• Base sizes for sporadic simple groups.
• Large orbits of supersolvable linear groups
• Regular orbits of linear groups with an application to the \(k(GV)\)-problem. I
• Orbits of permutation groups on the power set
• Orbit sizes, character degrees and Sylow subgroups.
• Bases of primitive linear groups.
• Regular orbits of solvable linear \(p'\)-groups.
• The minimal base size for a 𝑝-solvable linear group
• Blocks with equal height zero degrees
• On base sizes for symmetric groups
• Base sizes for simple groups and a conjecture of Cameron
• Large orbits in actions of nilpotent groups
• Simple groups, permutation groups, and probability
• Base Sizes and Regular Orbits for Coprime Affine Permutation Groups
• Small Groups of Automorphisms
• Primitive Groups with no Regular Orbits on the Set of Subsets
• Trivial Set-Stabilizers in Finite Permutation Groups
• The Minimal Base Size of Primitive Solvable Permutation Groups
• On Pyber’s base size conjecture
• On base sizes for actions of finite classical groups
• Large orbits in coprime actions of solvable groups
• [https://portal.mardi4nfdi.de/wiki/Publication:5513801 Groups with Normal, Solvable Hall p � -Subgroups]
• Endliche Gruppen I

This page was built for publication: Every coprime linear group admits a base of size two