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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Applications and adaptations of the low index subgroups procedure
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by Marston Conder and Peter Dobcsányi PDF
Math. Comp. 74 (2005), 485-497 Request permission


The low-index subgroups procedure is an algorithm for finding all subgroups of up to a given index in a finitely presented group $G$ and hence for determining all transitive permutation representations of $G$ of small degree. A number of significant applications of this algorithm are discussed, in particular to the construction of graphs and surfaces with large automorphism groups. Furthermore, three useful adaptations of the procedure are described, along with parallelisation of the algorithm. In particular, one adaptation finds all complements of a given finite subgroup (in certain contexts), and another finds all normal subgroups of small index in the group $G$. Significant recent applications of these are also described in some detail.
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Additional Information
  • Marston Conder
  • Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
  • MR Author ID: 50940
  • ORCID: 0000-0002-0256-6978
  • Email:
  • Peter Dobcsányi
  • Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
  • Email:
  • Received by editor(s): July 25, 2000
  • Received by editor(s) in revised form: June 16, 2003
  • Published electronically: May 7, 2004
  • © Copyright 2004 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 485-497
  • MSC (2000): Primary 20-04, 20F05
  • DOI:
  • MathSciNet review: 2085903