CHARACTERIZATION BY PRIME GRAPH OF PGL(2, pk) WHERE p AND k > 1 ARE ODD

DOI10.1142/S021819671000587XzbMath1216.20006OpenAlexW2150468910MaRDI QIDQ3069778

Zeinab Akhlaghi, Behrooz Khosravi, Maryam Khatami

Publication date: 19 January 2011

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s021819671000587x

zbMATH Keywords

finite simple groupsspectrarecognizabilityprime graphssets of element ordersprojective linear groups

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Finite simple groups and their classification (20D05) Simple groups: alternating groups and groups of Lie type (20D06)

Related Items (15)

QUASIRECOGNITION BY PRIME GRAPH OF SOME ORTHOGONAL GROUPS OVER THE BINARY FIELD ⋮ On the composition factors of a group with the same prime graph as B n (5) ⋮ Criterion of unrecognizability of a finite group by its Gruenberg-Kegel graph ⋮ Quasirecognition of E6(q) by the orders of maximal abelian subgroups ⋮ Groups with the same prime graph as the orthogonal group \(B_n(3)\). ⋮ Gruenberg-Kegel graphs: cut groups, rational groups and the prime graph question ⋮ Quasirecognition by prime graph of finite simple groups \(L_n(2)\) and \(U_n(2)\). ⋮ Recognition by prime graph of \(^2D_{2^m+1}(3)\). ⋮ Groups with the same orders of maximal abelian subgroups as \(A_2(q)\). ⋮ On recognizability of \(\mathrm{PSU}_3(q)\) by the orders of maximal abelian subgroups ⋮ Groups with the same prime graph as the simple group \(D_n(5)\). ⋮ On some Frobenius groups with the same prime graph as the almost simple group PGL(2,49) ⋮ Unnamed Item ⋮ Quasirecognition by prime graph of \(^2D_n(3^\alpha)\) where \(n=4m+1\geq 21\) and \(\alpha\) is odd ⋮ ON COMPOSITION FACTORS OF A GROUP WITH THE SAME PRIME GRAPH AS Ln(5)

Cites Work

• A characterization of the finite simple group \(L_{16}(2)\) by its prime graph.
• On the prime graph of \(\text{PSL}(2,p)\) where \(p>3\) is a prime number.
• Prime graph components of finite groups
• A Diophantine equation which arises in the theory of finite groups
• Certain embeddings among finite groups of Lie type
• An Adjacency Criterion for the Prime Graph of a Finite Simple Group
• PRIME GRAPH COMPONENTS OF FINITE SIMPLE GROUPS
• Spectra of finite linear and unitary groups
• n-RECOGNITION BY PRIME GRAPH OF THE SIMPLE GROUP PSL(2,q)
• A characterization of some alternating and symmetric groups
• The Prime Graph of a Sporadic Simple Group
• On integers with identical digits
• Endliche Gruppen I
• On a class of doubly transitive groups
• Prime graph components of the simple groups of Lie type over the field of even characteristic

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