On Holt's Algorithm
Copyright policy )On Holt's Algorithm
\textit{D. F. Holt} [Comput. group theory, Proc. Symp., Durham 1982, 307-319 (1984; Zbl 0544.20004)] has described an algorithm for the computation of the Schur multiplier of a permutation group \(G\). As one of the steps, after finding a Sylow subgroup \(P\) of \(G\), he needs a power-commutator presentation of \(P\) in order to use collection methods for the determination of the Schur multiplier of \(P\). In this paper the authors detail the method for finding for a \(p\)-group (given as a permutation group by base and strong generating set) a power-commutator presentation such that the generators contained in a group \(G_ i\) of the underlying composition series form a strong generating set for \(G_ i\).
- University of Sydney Australia
- University of Chicago United States
Generators, relations, and presentations of groups, collection methods, algorithm, permutation group, Algebra and Number Theory, Schur multiplier, strong generating set, power- commutator presentation, Sylow subgroup, Computational Mathematics, Computational methods (permutation groups), Finite nilpotent groups, \(p\)-groups, composition series, General theory for finite permutation groups, Software, source code, etc. for problems pertaining to group theory, base, Projective representations and multipliers, \(p\)-group, generators
Generators, relations, and presentations of groups, collection methods, algorithm, permutation group, Algebra and Number Theory, Schur multiplier, strong generating set, power- commutator presentation, Sylow subgroup, Computational Mathematics, Computational methods (permutation groups), Finite nilpotent groups, \(p\)-groups, composition series, General theory for finite permutation groups, Software, source code, etc. for problems pertaining to group theory, base, Projective representations and multipliers, \(p\)-group, generators
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