Characterization of \(\text{PGL}(2,p)\) by its order and one conjugacy class size.

DOI10.1007/s12044-015-0253-4zbMath1333.20010OpenAlexW2164347924MaRDI QIDQ902258

Yanheng Chen, Gui-Yun Chen

Publication date: 7 January 2016

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12044-015-0253-4

zbMATH Keywords

finite simple groupsThompson conjectureconjugacy class sizesprime graphssets of element ordersconjugacy class lengths

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Linear algebraic groups over finite fields (20G40) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Finite simple groups and their classification (20D05)

Cites Work

• Thompson's conjecture for some finite simple groups with connected prime graph.
• Thompson's conjecture for alternating group of degree 22.
• Recognizing \(L_2(p)\) by its order and one special conjugacy class size.
• Thompson's conjecture for Lie type groups \(E_7(q)\).
• A new characterization of \(\text{PGL}(2,p)\) by its noncommuting graph.
• A characterization of the alternating group \(A_{10}\) by its conjugacy class lengths.
• Thompson's conjecture for simple groups with connected prime graph.
• On Thompson's conjecture for some finite simple groups.
• Prime graph components of finite groups
• Further reflections on Thompson's conjecture
• On Thompson's conjecture
• On Thompson's conjecture.
• On the Validity of Thompson's Conjecture for Finite Simple Groups
• On Thompson's Conjecture ofA₁₀
• ON THE THOMPSON'S CONJECTURE ON CONJUGACY CLASSES SIZES
• On a problem of E. Artin
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