Classifying Finite Simple Groups with Respect to the Number of Orbits Under the Action of the Automorphism Group

DOI10.1081/AGB-200039279zbMath1077.20023OpenAlexW2060322795MaRDI QIDQ4678716

Stefan Kohl

Publication date: 23 May 2005

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

Full work available at URL: https://doi.org/10.1081/agb-200039279

zbMATH Keywords

conjugacy classesnumbers of orbitsfinite simple groupsautomorphism groups

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Automorphisms of abstract finite groups (20D45) Finite simple groups and their classification (20D05) Software, source code, etc. for problems pertaining to group theory (20-04)

Related Items (9)

Virtually nilpotent groups with finitely many orbits under automorphisms ⋮ Finite groups with six or seven automorphism orbits ⋮ Automorphism Orbits and Element Orders in Finite Groups: Almost-Solubility and the Monster ⋮ Soluble groups with few orbits under automorphisms ⋮ Unnamed Item ⋮ Automorphism group orbits on finite simple groups ⋮ On 9- and 10-decomposable finite groups. ⋮ On Finite Groups with Few Automorphism Orbits ⋮ FC-groups with finitely many automorphism orbits

Uses Software

• GAP
• GAP Character Table Library

Cites Work

• The conjugate classes of Chevalley groups of type \((G_2)\)
• On the computation of conjugacy classes of Chevalley groups
• COUNTING THE ORBITS ON FINITE SIMPLE GROUPS UNDER THE ACTION OF THE AUTOMORPHISM GROUP – SUZUKI GROUPS VS. LINEAR GROUPS
• Numbers of conjugacy classes in some finite classical groups

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