@inproceedings{6224dca70a8e41d982b1a0232a606377,

title = "Conway's groupoid and its relatives",

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.",

keywords = "math.GR, 20B15 (Primary) 20B25, 05B05 (Secondary), code, design, groupoid, hypergraph, M13 , permutation group, projective plane, two-graph",

author = "Nick Gill and Jason Semeraro and Gillespie, {Neil I.} and Praeger, {Cheryl E.}",

note = "18 pages. Submitted to proceedings of the 2015 conference {"}Finite Simple Groups: Thirty Years of the Atlas and Beyond{"}; Finite Simple Groups: Thirty Years of the Atlas and Beyond : Celebrating the Atlases and Honoring John Conway ; Conference date: 02-11-2015 Through 05-11-2015",

year = "2017",

doi = "10.1090/conm/694/13962",

language = "English",

isbn = "978-1-4704-3678-0",

volume = "694",

series = "Contemporary Mathematics",

publisher = "American Mathematical Society",

editor = "Manjul Bhargava and Robert Guralnick and Gerard Hiss and Klaus Lux and Tiepp, {Pham Huu}",

booktitle = "Finite Simple Groups",

}