A new characterization of Mathieu-groups by the order and one irreducible character degree.

DOI10.1186/1029-242X-2013-209zbMath1284.20013WikidataQ59301522 ScholiaQ59301522MaRDI QIDQ394600

Yan Xiong Yan, Hai Jing Xu, Gui-Yun Chen

Publication date: 27 January 2014

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

zbMATH Keywords

finite simple groupscharacter degreescomplex irreducible charactersMathieu groups

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Simple groups: sporadic groups (20D08) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Representations of sporadic groups (20C34)

Related Items (14)

A new characterization for some extensions of \(\mathrm{PSL}(2,q)\) for some \(q\) by some character degrees. ⋮ Recognizing the automorphism groups of Mathieu groups through their orders and large degrees of their irreducible characters. ⋮ A new characterization of L2(p3) ⋮ A new characterization of the automorphism groups of Mathieu groups ⋮ Characterization of \(\mathrm{PGL}(2, p^2)\) by order and some irreducible character degrees ⋮ Recognition of \(M \times M\) by its complex group algebra where \(M\) is a simple \(K_3\)-group ⋮ Recognition of PSL(2,p) ×PSL(2,p) by its complex group algebra ⋮ Recognition of the simple group \(\mathrm{PSL}(2,p^2)\) by character degree graph and order. ⋮ A characterization of linear groups \(L_3(q)\) by their character degree graphs and orders ⋮ Recognition of the simple group \(\mathrm {PSL}(2, p)\) by one character degree and order ⋮ Recognition of \(L_2(q)\) by its group order and largest irreducible character degree. ⋮ A new characterization of \(L_2(p^2)\) ⋮ A CHARACTERIZATION OF PSL(4,p) BY SOME CHARACTER DEGREE ⋮ Mathieu groups and its degree prime-power graphs

Cites Work

• On Huppert's conjecture for \(G_2(q)\), \(q\geq 7\).
• Verifying Huppert's Conjecture for PSL₃(q) and PSU₃(q²)

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