Graph isomorphism problem and \(2\)-closed permutation groups

DOI10.1007/BF01196622zbMath0803.20003MaRDI QIDQ1311608

Ilya Nikolaevich Ponomarenko

Publication date: 4 January 1995

Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)

zbMATH Keywords

polynomial time algorithmcoherent configurations2-closed permutation groupsgraph isomorphism problemalgorithmic problems2-closurestrong generating setnilpotent permutation group

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Generators, relations, and presentations of groups (20F05) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) General theory for finite permutation groups (20B05)

Related Items (7)

Closures of finite permutation groups ⋮ Two-closure of rank \(3\) groups in polynomial time ⋮ On computing the closures of solvable permutation groups ⋮ Finite nilpotent groups that coincide with their 2-closures in all of their faithful permutation representations ⋮ The 2-closure of a \(\frac{3}{2}\)-transitive group in polynomial time ⋮ Two-closures of supersolvable permutation groups in polynomial time ⋮ On finite totally \(2\)-closed groups

Cites Work

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• Sylow's theorem in polynomial time
• A polynomial bound for the orders of primitive solvable groups
• Isomorphism of graphs of bounded valence can be tested in polynomial time
• A note on the graph isomorphism counting problem
• On the 2-Closures of Finite Permutation Groups

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