Isomorphism testing for \(p\)-groups

DOI10.1006/jsco.1994.1007zbMath0824.20020OpenAlexW1989359050MaRDI QIDQ1333168

E. A. O'Brien

Publication date: 30 October 1995

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

Full work available at URL: https://doi.org/10.1006/jsco.1994.1007

zbMATH Keywords

performancefinite \(p\)-groupsimplementationlower central seriesgenerators of automorphism groupsisomorphism testingstandard presentationslower exponent-\(p\) central seriesextensions of \(p\)-groups\(p\)-quotient algorithmconstruction of isomorphismsimmediate descendantspower commutator presentationsstandard \(p\)-group generation algorithm

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Generators, relations, and presentations of groups (20F05) Parallel algorithms in computer science (68W10) Automorphisms of abstract finite groups (20D45) Finite nilpotent groups, (p)-groups (20D15) Software, source code, etc. for problems pertaining to group theory (20-04) Derived series, central series, and generalizations for groups (20F14)

Related Items (19)

On the Efficiency of Some Finite Groups ⋮ Certain cyclically presented groups are isomorphic ⋮ Algorithms for Group Isomorphism via Group Extensions and Cohomology ⋮ Groups and nilpotent Lie rings whose order is the sixth power of a prime. ⋮ On the Complexity of Isomorphism Problems for Tensors, Groups, and Polynomials I: Tensor Isomorphism-Completeness ⋮ A MILLENNIUM PROJECT: CONSTRUCTING SMALL GROUPS ⋮ Tensor isomorphism by conjugacy of Lie algebras ⋮ CONSTRUCTING AUTOMORPHISM GROUPS OF p-GROUPS ⋮ The Solvable Primitive Permutation Groups of Degree at Most 6560 ⋮ Practical post-quantum signature schemes from isomorphism problems of trilinear forms ⋮ General linear group action on tensors: a candidate for post-quantum cryptography ⋮ Heuristics for 2-class Towers of Cyclic Cubic Fields ⋮ Filters compatible with isomorphism testing ⋮ Beating the generator-enumeration bound for \(p\)-group isomorphism ⋮ A fast isomorphism test for groups whose Lie algebra has genus 2 ⋮ Computing automorphism groups and testing isomorphisms for modular group algebras. ⋮ Computing 2-cocyeles for central extensions and relative difference sets ⋮ ON THE CLASSIFICATION OF GROUPS OF PRIME-POWER ORDER BY COCLASS: THE 3-GROUPS OF COCLASS 2 ⋮ The groups with order \(p^7\) for odd prime \(p\).

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