Fast constructive recognition of a black box group isomorphic to \(S_n\) or \(A_n\) using Goldbach's conjecture

DOI10.1006/jsco.1999.0295zbMath0952.20005OpenAlexW1979045682WikidataQ123226193 ScholiaQ123226193MaRDI QIDQ1971492

Igor Pak, Sergey Bratus

Publication date: 28 August 2000

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jsco.1999.0295

zbMATH Keywords

symmetric groupsfinitely generated groupsalternating groupsrandomized algorithmscomplexity estimatesgroup isomorphismsGoldbach conjecture

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Goldbach-type theorems; other additive questions involving primes (11P32)

Related Items

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, Computing maximal subgroups of finite groups., Computers as a novel mathematical reality. IV: The Goldbach problem, Fast recognition of alternating groups of unknown degree., Applications of character estimates to statistical problems for symmetric group, A practical model for computation with matrix groups., THE ANDREWS–CURTIS CONJECTURE AND BLACK BOX GROUPS, Computing a Chief Series and the Soluble Radical of a Matrix Group Over a Finite Field, Generalised Sifting in Black-Box Groups, Constructive recognition of finite alternating and symmetric groups acting as matrix groups on their natural permutation modules.

Uses Software

• GAP

Cites Work

• Fast recognition of doubly transitive groups
• Walks on generating sets of groups
• On Vinogradov's constant in Goldbach's ternary problem
• Approximate formulas for some functions of prime numbers
• A Recognition Algorithm for Special Linear Groups
• The exceptional set of Goldbach's problem
• A.D. Alexandrov spaces with curvature bounded below
• A Recognition Algorithm For Classical Groups Over Finite Fields
• A complete Vinogradov 3-primes theorem under the Riemann hypothesis
• Checking the odd Goldbach conjecture up to 10²⁰
• Generating random elements of a finite group
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