Bases of primitive linear groups.

DOI10.1016/S0021-8693(02)00001-7zbMath1034.20001MaRDI QIDQ1849092

Martin W. Liebeck, Aner Shalev

Publication date: 28 November 2002

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

zbMATH Keywords

tensor productssemidirect productsprimitive linear groupsfinite primitive permutation groupsbase sizesPyber's conjecture

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Representations of finite groups of Lie type (20C33) Primitive groups (20B15)

Related Items (16)

Base sizes of imprimitive linear groups and orbits of general linear groups on spanning tuples ⋮ Abelian quotients and orbit sizes of solvable linear groups ⋮ A proof of Pyber's base size conjecture ⋮ Bases of twisted wreath products ⋮ Orbit sizes and the central product group of order 16 ⋮ A Faster Isomorphism Test for Graphs of Small Degree ⋮ Counting irreducible modules for profinite groups ⋮ Random generation of finite and profinite groups and group enumeration. ⋮ Orbit sizes and the dihedral group of order eight ⋮ Bases for quasisimple linear groups ⋮ Base sizes of primitive groups: bounds with explicit constants ⋮ Bases of primitive linear groups. II. ⋮ Every coprime linear group admits a base of size two ⋮ The minimal base size for a 𝑝-solvable linear group ⋮ An improved diameter bound for finite simple groups of Lie type ⋮ On Pyber’s base size conjecture

Cites Work

• Upper bounds for the number of conjugacy classes of a finite group
• Bases for primitive permutation groups and a conjecture of Babai
• Intersections of matrix algebras and permutation representation of \(\text{PSL}(n,q)\)
• The local structure of finite groups of characteristic 2 type
• Generators for Finite Simple Groups, with Applications to Linear Groups
• Simple groups, permutation groups, and probability
• Base Sizes and Regular Orbits for Coprime Affine Permutation Groups
• Small Degree Representations of Finite Chevalley Groups in Defining Characteristic
• The Minimal Base Size of Primitive Solvable Permutation Groups
• Diameters of finite simple groups: sharp bounds and applications
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