Conway’s groupoid and its relatives
| Autor: | Nick Gill, Neil I. Gillespie, Cheryl E. Praeger, Jason Semeraro |
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| Rok vydání: | 2017 |
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| Zdroj: | Finite Simple Groups: Thirty Years of the Atlas and Beyond. :91-110 |
| ISSN: | 1098-3627 0271-4132 |
| Popis: | In 1987, John Horton Conway constructed a subset $M_{13}$ of permutations on a set of size $13$ for which the subset fixing any given point is isomorphic to the Mathieu group $M_{12}$. The construction has fascinated mathematicians for the past thirty years, and remains remarkable in its mathematical isolation. It is based on a ``moving-counter puzzle'' on the projective plane $\PG(2,3)$. This survey, a homage to John Conway and his mathematics, discusses consequences and generalisations of Conway's construction. In particular it explores how various designs and hypergraphs can be used instead of $\PG(2,3)$ to obtain interesting analogues of $M_{13}$. In honour of John Conway, we refer to these analogues as {\it Conway groupoids}. A number of open questions are presented. |
| Databáze: | OpenAIRE |
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