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The transitive groups of degree 48 and some applications
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Holt, Derek F., Royle, Gordon and Tracey, Gareth M. (2022) The transitive groups of degree 48 and some applications. Journal of Algebra, 6077 (Part A). pp. 372-386. doi:10.1016/j.jalgebra.2021.06.018 ISSN 0021-8693.
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Official URL: https://doi.org/10.1016/j.jalgebra.2021.06.018
Abstract
The primary purpose of this paper is to report on the successful enumeration in Magma of representatives of the conjugacy classes of transitive subgroups of the symmetric group of degree 48. In addition, we have determined that 25707 of these groups are minimal transitive and that 713 of them are elusive. The minimal transitive examples have been used to enumerate the vertex-transitive groups of degree 48, of which there are , all but 0.1625% of which arise as Cayley graphs. We have also found that the largest number of elements required to generate any of these groups is 10, and we have used this fact to improve previous general bounds of the third author on the number of elements required to generate an arbitrary transitive permutation group of a given degree. The details of the proof of this improved bound will be published as a separate paper.
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| SWORD Depositor: | Library Publications Router | ||||||||
| Library of Congress Subject Headings (LCSH): | Magma (Computer file), Subgroup growth (Mathematics), Cayley graphs , Algebra -- Data processing, Group theory | ||||||||
| Journal or Publication Title: | Journal of Algebra | ||||||||
| Publisher: | Elsevier | ||||||||
| ISSN: | 0021-8693 | ||||||||
| Official Date: | 1 October 2022 | ||||||||
| Dates: |
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| Volume: | 6077 | ||||||||
| Number: | Part A | ||||||||
| Page Range: | pp. 372-386 | ||||||||
| DOI: | 10.1016/j.jalgebra.2021.06.018 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 12 July 2021 | ||||||||
| Date of first compliant Open Access: | 29 June 2022 |
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