Conway's groupoid and its relatives

Nick Gill, Neil Gillespie, Cheryl E. Praeger, Jason Semeraro

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

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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.
Original languageEnglish
Title of host publicationFinite Simple Groups
Subtitle of host publicationThirty Years of the Atlas and Beyond
Place of PublicationPrinceton, NJ
PublisherAmerican Mathematical Society
ISBN (Electronic)9781470441685
ISBN (Print)9781470436780
Publication statusPublished - 2017
EventFinite Simple Groups: Thirty Years of the Atlas and Beyond - Princeton, New Jersey, United States
Duration: 2 Nov 20155 Nov 2015

Publication series

NameContemporary Mathematics
PublisherAmerican Mathematical Society
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627


ConferenceFinite Simple Groups
Country/TerritoryUnited States
CityPrinceton, New Jersey


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