Thompson's conjecture for Lie type groups \(E_7(q)\).

DOI10.1007/s11425-013-4663-4zbMath1312.20009OpenAlexW2081658347WikidataQ115378101 ScholiaQ115378101MaRDI QIDQ476736

Mingchun Xu, Wujie Shi

Publication date: 2 December 2014

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-013-4663-4

zbMATH Keywords

conjugacy classesfinite simple groupscentralizersfinite groups of Lie typeconjugacy class sizesprime graphssets of element ordersminimal normal subgroups

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Simple groups: alternating groups and groups of Lie type (20D06)

Related Items

Characterization of \(\text{PGL}(2,p)\) by its order and one conjugacy class size. ⋮ On Thompson's conjecture for finite simple exceptional groups of Lie type ⋮ On Thompson’s conjecture for finite simple groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Cocliques of maximal size in the prime graph of a finite simple group
• On Thompson's conjecture for some finite simple groups.
• On the length of the conjugacy classes of finite groups
• Prime graph components of finite groups
• Further reflections on Thompson's conjecture
• On Thompson's conjecture
• On Thompson's conjecture.
• Generators for Simple Groups
• An Adjacency Criterion for the Prime Graph of a Finite Simple Group
• On Large Zsigmondy Primes
• Composition Factors from the Group Ring and Artin's Theorem on Orders of Simple Groups
• The Maximal Tori in The Finite Chevalley Groups of Type E₆E₇And E₈
• The semisimple conjugacy classes of finite groups of lie type E₆and E₇
• Matrix generators for exceptional groups of Lie type
• A characterization of the finite simple groups