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Algorithms for polycyclic-by-finite groups
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Sinanan, S. K. and Holt, Derek F. (2017) Algorithms for polycyclic-by-finite groups. Journal of Symbolic Computation, 79 (Part 2). pp. 269-284. doi:10.1016/j.jsc.2016.02.008 ISSN 0747-7171.
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Official URL: http://dx.doi.org/10.1016/j.jsc.2016.02.008
Abstract
A set of fundamental algorithms for computing with polycyclic-by-finite groups is presented. Polycyclic-by-finite groups arise naturally in a number of contexts; for example, as automorphism groups of large finite soluble groups, as quotients of finitely presented groups, and as extensions of modules by groups. No existing mode of representation is suitable for these groups, since they will typically not have a convenient faithful permutation representation. A mixed mode is used to represent elements of such a group, utilising either a power-conjugate presentation or a polycyclic presentation for the elements of the normal subgroup, and a permutation representation for the elements of the quotient.
| Item Type: | Journal Article | ||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||
| Library of Congress Subject Headings (LCSH): | Polycyclic groups, Finite groups | ||||||||||
| Journal or Publication Title: | Journal of Symbolic Computation | ||||||||||
| Publisher: | Elsevier Science Ltd. / Academic Press Ltd. | ||||||||||
| ISSN: | 0747-7171 | ||||||||||
| Official Date: | March 2017 | ||||||||||
| Dates: |
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| Volume: | 79 | ||||||||||
| Number: | Part 2 | ||||||||||
| Page Range: | pp. 269-284 | ||||||||||
| DOI: | 10.1016/j.jsc.2016.02.008 | ||||||||||
| Status: | Peer Reviewed | ||||||||||
| Publication Status: | Published | ||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||
| Date of first compliant deposit: | 25 February 2016 | ||||||||||
| Date of first compliant Open Access: | 11 August 2017 | ||||||||||
| Funder: | University of Warwick Postgraduate Research Scholarship, University of Warwick Vice Chancellor Scholarship, Engineering and Physical Sciences Research Council (EPSRC) |
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