On the length of subgroup chains in the symmetric group

DOI10.1080/00927878608823393zbMath0604.20004OpenAlexW2125647096MaRDI QIDQ3741778

László Babai

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1080/00927878608823393

zbMATH Keywords

complexitypermutation group algorithmslength of subgroup chainorder of primitive permutation groups

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Series and lattices of subgroups (20D30) Software, source code, etc. for problems pertaining to group theory (20-04) Primitive groups (20B15) Subgroups of symmetric groups (20B35)

Related Items (20)

The length and depth of algebraic groups ⋮ Asymmetric coloring of locally finite graphs and profinite permutation groups: Tucker's conjecture confirmed ⋮ Almost simplep-obstructions in odd characteristic lie type groups^∗ ⋮ Walks on generating sets of Abelian groups ⋮ On-the-fly bisimilarity checking for fresh-register automata ⋮ Formations of finite groups in polynomial time: \(\mathfrak{F}\)-residuals and \(\mathfrak{F}\)-subnormality ⋮ The depth of a finite simple group ⋮ Computing the order of a solvable permutation group ⋮ The ring of \(k\)-regular sequences. II. ⋮ Most primitive groups are full automorphism groups of edge-transitive hypergraphs. ⋮ Efficient representation of perm groups ⋮ Polynomial-time equivalence testing for deterministic fresh-register automata ⋮ On the diameter of permutation groups ⋮ Chains of subsemigroups ⋮ On the orders of doubly transitive permutation groups, elementary estimates ⋮ Efficient Computation of the Fourier Transform on Finite Groups ⋮ The length and depth of associative algebras ⋮ Chains of subgroups in symmetric groups ⋮ Lower bounds on the Noether number ⋮ Growth in groups: ideas and perspectives

Cites Work

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• Sylow's theorem in polynomial time
• On the order of doubly transitive permutation groups
• On the order of uniprimitive permutation groups
• Isomorphism of graphs of bounded valence can be tested in polynomial time
• Permutation representations
• The transitive groups of degree up to eleven⁺
• A compact representation for permutation groups
• Polynomial-time algorithms for finding elements of prime order and sylow subgroups
• On the orders of Primitive Permutation Groups
• Finite Permutation Groups and Finite Simple Groups

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