Criterion of unrecognizability of a finite group by its Gruenberg-Kegel graph

DOI10.1016/j.jalgebra.2021.12.005OpenAlexW3107709128MaRDI QIDQ2153307

Peter J. Cameron, Natal'ya Vladimirovna Maslova

Publication date: 4 July 2022

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

Full work available at URL: https://arxiv.org/abs/2012.01482

zbMATH Keywords

finite groupalmost simple groupGruenberg-Kegel graph (prime graph)recognition by Gruenberg-Kegel graph (prime graph)

Mathematics Subject Classification ID

Group theory and generalizations (20-XX) Associative rings and algebras (16-XX)

Related Items (16)

Super graphs on groups. I ⋮ Matching in power graphs of finite groups ⋮ On the prime graph of a finite group with unique nonabelian composition factor ⋮ Solvable conjugacy class graph of groups ⋮ On characterization by Gruenberg-Kegel graph of finite simple exceptional groups of Lie type ⋮ Classification of non-solvable groups whose power graph is a cograph ⋮ Primitive prime divisors of orders of Suzuki-Ree groups ⋮ Shunkov groups saturated with almost simple groups ⋮ Gruenberg-Kegel graphs: cut groups, rational groups and the prime graph question ⋮ Unnamed Item ⋮ Enhanced power graphs of groups are weakly perfect ⋮ On finite groups whose power graph is a cograph ⋮ Graphs defined on groups ⋮ Co-degree graphs and order elements ⋮ Recent developments on the power graph of finite groups – a survey ⋮ \text{M}, \text{B} and \(\mathrm{Co}_1\) are recognisable by their prime graphs

Uses Software

• ATLAS Group Representations

Cites Work

• On a class of doubly transitive groups
• Prime graph components of the simple groups of Lie type over the field of even characteristic
• Between the enhanced power graph and the commuting graph
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• Finite groups with a five-component prime graph.
• Groups with the same prime graph as the orthogonal group \(B_n(3)\).
• On \(r\)-recognition by prime graph of \(B_p(3)\) where \(p\) is an odd prime.
• Characterization of the finite simple groups by spectrum and order.
• Quasirecognition by the prime graph of \(L_3(q)\) where \(3<q<100\).
• On finite tetraprimary groups.
• 2-recognizability of the simple groups \(B_n(3)\) and \(C_n(3)\) by prime graph.
• On finite groups isospectral to simple classical groups.
• On finite groups with disconnected prime graph.
• Recognition of the groups \(E_7(2)\) and \(E_7(3)\) by prime graph
• A characterization of the prime graphs of solvable groups.
• On the structure of finite groups isospectral to finite simple groups.
• Quasirecognition by prime graph of \(F_4(q)\) where \(q=2^n>2\).
• On recognizability of some finite simple orthogonal groups by spectrum.
• Quasirecognition by the prime graph of the group \(C_n(2)\), where \(n\neq 3\) is odd.
• Quasirecognition by prime graph of finite simple groups \(L_n(2)\) and \(U_n(2)\).
• Recognition by prime graph of \(^2D_{2^m+1}(3)\).
• Characterizations of the simple group \(^2D_n(3)\) by prime graph and spectrum.
• A criterion of unrecognizability by spectrum for finite groups.
• Cocliques of maximal size in the prime graph of a finite simple group
• Quasirecognition by prime graph of the simple group \(B_n(2)\).
• On groups of even order
• Uniqueness of the prime graph of \(L_{16}(2)\).
• On groups critical with respect to a set of natural numbers.
• On realizability of a graph as the prime graph of a finite group
• 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.
• Quasirecognition by prime graph of the simple group \(^2F_4(q)\).
• Prime graph components of finite groups
• The set of orders of elements in a finite group
• Recognition of alternating groups of prime degree from their element orders
• On spectra of almost simple extensions of even-dimensional orthogonal groups
• Finite almost simple groups whose Gruenberg-Kegel graphs coincide with Gruenberg-Kegel graphs of solvable groups
• Quasirecognition by prime graph of the groups \(^2 D_{2n}(q)\) where \(q<10^5\)
• On recognition of alternating groups by prime graph
• Characterization of the group \(G_2(5)\) by the prime graph
• Corrigendum to: Prime graph components of the simple groups of Lie type over the field of even characteristic
• Characterization of groups with non-simple socle
• On element orders in covers of \(L_4(q)\) and \(U_4(q)\)
• On recognition of \(L_4(q)\) and \(U_4(q)\) by spectrum
• On recognition of the sporadic simple groups \(HS\), \(J_3\), \(Suz\), \(O'N\), \(Ly\), \(Th\), \(Fi_{23}\), and \(Fi'_{24}\) by the Gruenberg-Kegel graph
• Groups with the same prime graph as the simple group \(D_n(5)\).
• Quasirecognition by prime graph of \(^2D_n(3^\alpha)\) where \(n=4m+1\geq 21\) and \(\alpha\) is odd
• Finite groups whose prime graphs do not contain triangles. II
• On the structure of the power graph and the enhanced power graph of a group
• 2-quasirecognizability of the simple groups \(B_n(p)\) and \(C_n(p)\) by prime graph.
• On the coincidence of Grünberg-Kegel graphs of a finite simple group and its proper subgroup.
• On the realizability of a graph as the Gruenberg-Kegel graph of a finite group
• On recognition by spectrum of symmetric groups.
• Unsolved Problems in Group Theory. The Kourovka Notebook
• QUASIRECOGNITION BY PRIME GRAPH OF SOME ORTHOGONAL GROUPS OVER THE BINARY FIELD
• On the prime graph of D_n(q) where q ∊ {2, 5}
• On recognition by prime graph of the projective special linear group over GF(3)
• QUASIRECOGNITION BY PRIME GRAPH OF THE SIMPLE GROUPS G₂(q) AND ²B₂(q)
• CHARACTERIZATION BY PRIME GRAPH OF PGL(2, p^k) WHERE p AND k > 1 ARE ODD
• On the composition factors of a group with the same prime graph as B n (5)
• An Adjacency Criterion for the Prime Graph of a Finite Simple Group
• Recognition of simple groups U 3(Q) by element orders
• PRIME GRAPH COMPONENTS OF FINITE SIMPLE GROUPS
• Quasirecognition by prime graph of some alternating groups
• n-RECOGNITION BY PRIME GRAPH OF THE SIMPLE GROUP PSL(2,q)
• Decomposition of the Augmentation Ideal and of the Relation Modules of a Finite Group
• The diameter of the prime graph of a finite group
• The Prime Graph of a Sporadic Simple Group
• Finite simple unisingular groups of Lie type
• Recognition of the simple groups L3(q) by element orders
• Quasirecognition by prime graph of simple group D_n(3)
• On groups having the prime graph as alternating and symmetric groups
• The group J4 × J4 is recognizable by spectrum
• A study of enhanced power graphs of finite groups
• On almost recognizability by spectrum of simple classical groups
• Recognition of symplectic and orthogonal groups of small dimensions by spectrum
• ON THE PRIME GRAPH OF SIMPLE GROUPS
• Recognition of finite groups by the prime graph
• On quasirecognition by prime graph of the simple groups $A^{+}_{n}(p)$ and $A^{-}_{n}(p)$
• On 2-Modular Representations of the Suzuki Groups
• Groups Having Strongly Self-Centralizing 3-Centralizers

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