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Title: Conway’s groupoid and its relatives
Authors: Gill, Nick
Gillespie, Neil I.
Praeger, Cheryl E.
Semeraro, Jason
First Published: 1-Jun-2017
Presented at: Finite Simple Groups: Thirty Years of the Atlas and Beyond
Publisher: American Mathematical Society
Citation: Finite Simple Groups: Thirty Years of the Atlas and Beyond, 2017
Abstract: In 1997, John Conway constructed a 6-fold transitive subset M13 of permutations on a set of size 13 for which the subset fixing any given point was isomorphic to the Mathieu group M12. The construction was via a “moving-counter puzzle” on the projective plane PG(2, 3). We discuss consequences and generalisations of Conway’s construction. In particular we explore how various designs and hypergraphs can be used instead of PG(2, 3) to obtain interesting analogues of M13; we refer to these analogues as Conway groupoids. A number of open questions are presented.
ISBN: 978-1-4704-3678-0
Embargo on file until: 1-Jan-10000
Version: Post-print
Status: Peer-reviewed
Type: Conference Paper
Rights: Copyright © 2017, American Mathematical Society. Deposited with reference to the publisher’s open access archiving policy. (
Description: The file associated with this record is under embargo while permission to archive is sought from the publisher. The full text may be available through the publisher links provided above.
Appears in Collections:Conference Papers & Presentations, Dept. of Mathematics

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