A black-box group algorithm for recognizing finite symmetric and alternating groups, I

DOI10.1090/S0002-9947-03-03040-XzbMath1022.20004OpenAlexW1854352062MaRDI QIDQ4794618

Robert Beals, Cheryl E. Praeger, Seress, Ákos, Alice C. Niemeyer, Charles R. Leedham-Green

Publication date: 19 February 2003

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-03-03040-x

zbMATH Keywords

symmetric groupsalternating groupsrecognitionpermutation representationsblack-box groupsLas Vegas algorithmsgroup theoretic algorithms

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Symbolic computation and algebraic computation (68W30) Symmetric groups (20B30) Probabilistic methods in group theory (20P05)

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Construction of the outer automorphism of \(\mathcal {S}_{6}\) via a complex Hadamard matrix ⋮ A black-box group algorithm for recognizing finite symmetric and alternating groups, I ⋮ Identifying long cycles in finite alternating and symmetric groups acting on subsets ⋮ Prime power graphs for groups of Lie type ⋮ FINDING INVOLUTIONS WITH SMALL SUPPORT ⋮ Fast Constructive Recognition of Black-Box Unitary Groups ⋮ RECOGNITION OF SMALL DIMENSIONAL REPRESENTATIONS OF GENERAL LINEAR GROUPS ⋮ Fast recognition of alternating groups of unknown degree. ⋮ Constructive membership in black-box groups ⋮ Constructing Maximal Subgroups of Classical Groups ⋮ On the twisted modules for finite matrix groups ⋮ On permutations of order dividing a given integer ⋮ Short presentations for alternating and symmetric groups ⋮ On the frequency of permutations containing a long cycle. ⋮ Large element orders and the characteristic of Lie-type simple groups. ⋮ Constructive recognition of classical groups in odd characteristic. ⋮ Permutations with orders coprime to a given integer ⋮ Black box exceptional groups of Lie type ⋮ Generalised Sifting in Black-Box Groups ⋮ Constructive recognition of finite alternating and symmetric groups acting as matrix groups on their natural permutation modules.

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