Applications and adaptations of the low index subgroups procedure

Authors:
Marston Conder and Peter Dobcsányi

Journal:
Math. Comp. **74** (2005), 485-497

MSC (2000):
Primary 20-04, 20F05

DOI:
https://doi.org/10.1090/S0025-5718-04-01647-3

Published electronically:
May 7, 2004

MathSciNet review:
2085903

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The low-index subgroups procedure is an algorithm for finding all subgroups of up to a given index in a finitely presented group and hence for determining all transitive permutation representations of 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 . 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

Email:
conder@math.auckland.ac.nz

**Peter Dobcsányi**

Affiliation:
Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand

Email:
peter@math.auckland.ac.nz

DOI:
https://doi.org/10.1090/S0025-5718-04-01647-3

Keywords:
Finitely presented groups,
algorithms,
low index subgroups

Received by editor(s):
July 25, 2000

Received by editor(s) in revised form:
June 16, 2003

Published electronically:
May 7, 2004

Article copyright:
© Copyright 2004
American Mathematical Society