Characteristic covering numbers of finite simple groups

DOI10.1007/s00208-022-02520-7arXiv2101.02682OpenAlexW3118443452MaRDI QIDQ6184758

Pham Hũ'u Tiêp, Michael J. Larsen, Aner Shalev

Publication date: 29 January 2024

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.02682

zbMATH Keywords

covering numberfinite simple groupword map

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Simple groups: alternating groups and groups of Lie type (20D06)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Products of conjugacy classes in finite unitary groups \(\mathrm{GU}(3,q^2)\) and \(\mathrm{SU}(3,q^2)\).
• The covering numbers of the sporadic simple groups
• The Waring problem for finite simple groups.
• Products of powers in finite simple groups
• SL(V) is 4-reflectional
• On free subgroups of semi-simple groups
• Caractères unipotents de \({}^ 3D_ 4({\mathbb{F}}_ q)\)
• Word maps, conjugacy classes, and a noncommutative Waring-type theorem.
• The Ore conjecture.
• Characters of symmetric groups: sharp bounds and applications.
• On the minimal degrees of projective representations of the finite Chevalley groups
• Surjective word maps and Burnside's \(p^aq^b\) theorem
• The involution width of finite simple groups
• Fibers of automorphic word maps and an application to composition factors
• Word maps have large image.
• Fuchsian groups, coverings of Riemann surfaces, subgroup growth, random quotients and random walks.
• CHEVIE -- A system for computing and processing generic character tables
• On the \(p\)-width of finite simple groups
• Products of conjugacy classes in groups
• Even permutations as a product of two conjugate cycles
• WORDS WITH FEW VALUES IN FINITE SIMPLE GROUPS
• Word maps and Waring type problems
• Products of conjugacy classes and fixed point spaces
• Effective results on the Waring problem for finite simple groups
• Prime divisors of character degrees
• Character Table and Blocks of Finite Simple Triality Groups 3 D 4 (q)
• Subgroups of Maximal Rank in Finite Exceptional Groups of Lie Type
• The semisimple conjugacy classes of finite groups of lie type E₆and E₇
• On the conjectures of J. Thompson and O. Ore
• The semisimple conjugacy classes and the generic class number of the finite simple groups of lie type E₈
• A note on powers in simple groups
• Commutators in Finite Simple Groups of Lie Type
• Fibers of word maps and the multiplicities of non-abelian composition factors
• Real conjugacy classes in algebraic groups and finite groups of Lie type
• Primes in arithmetic progressions
• Products of squares in finite simple groups
• Some Results and Problems in the Theory of Word Maps
• Diameters of finite simple groups: sharp bounds and applications
• Products of normal subsets