Generating groups using hypergraphs

Nick Gill; Neil I. Gillespie; Anthony Nixon; Jason Semeraro

doi:10.1093/qmath/haw001

Generating groups using hypergraphs

Nick Gill, Neil I. Gillespie, Anthony Nixon, Jason Semeraro

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Allbwn ymchwil: Cyfraniad at gyfnodolyn › Erthygl › adolygiad gan gymheiriaid

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To a set B of 4-subsets of a set of size n, we introduce an invariant called the ‘hole stabilizer’ which generalizes a construction of Conway, Elkies and Martin of the Mathieu group M12 based on Lloyd’s ‘15-puzzle’. It is shown that hole stabilizers may be regarded as objects inside an objective partial group (in the sense of Chermak). We classify pairs (,B) with a trivial hole stabilizer, and determine all hole stabilizers associated to 2-(n, 4, λ) designs with λ 2.

Iaith wreiddiol	Saesneg
Tudalennau (o-i)	29-52
Nifer y tudalennau	24
Cyfnodolyn	Quarterly Journal of Mathematics
Cyfrol	67
Rhif cyhoeddi	1
Dynodwyr Gwrthrych Digidol (DOIs)	https://doi.org/10.1093/qmath/haw001
Statws	Cyhoeddwyd - 7 Maw 2016

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10.1093/qmath/haw001Trwydded: CC BY-NC-ND

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title = "Generating groups using hypergraphs",

abstract = "To a set B of 4-subsets of a set of size n, we introduce an invariant called the {\textquoteleft}hole stabilizer{\textquoteright} which generalizes a construction of Conway, Elkies and Martin of the Mathieu group M12 based on Lloyd{\textquoteright}s {\textquoteleft}15-puzzle{\textquoteright}. It is shown that hole stabilizers may be regarded as objects inside an objective partial group (in the sense of Chermak). We classify pairs (,B) with a trivial hole stabilizer, and determine all hole stabilizers associated to 2-(n, 4, λ) designs with λ 2.",

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author = "Nick Gill and Gillespie, {Neil I.} and Anthony Nixon and Jason Semeraro",

note = "16 pages",

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doi = "10.1093/qmath/haw001",

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AU - Gill, Nick

AU - Gillespie, Neil I.

AU - Nixon, Anthony

AU - Semeraro, Jason

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Y1 - 2016/3/7

N2 - To a set B of 4-subsets of a set of size n, we introduce an invariant called the ‘hole stabilizer’ which generalizes a construction of Conway, Elkies and Martin of the Mathieu group M12 based on Lloyd’s ‘15-puzzle’. It is shown that hole stabilizers may be regarded as objects inside an objective partial group (in the sense of Chermak). We classify pairs (,B) with a trivial hole stabilizer, and determine all hole stabilizers associated to 2-(n, 4, λ) designs with λ 2.

AB - To a set B of 4-subsets of a set of size n, we introduce an invariant called the ‘hole stabilizer’ which generalizes a construction of Conway, Elkies and Martin of the Mathieu group M12 based on Lloyd’s ‘15-puzzle’. It is shown that hole stabilizers may be regarded as objects inside an objective partial group (in the sense of Chermak). We classify pairs (,B) with a trivial hole stabilizer, and determine all hole stabilizers associated to 2-(n, 4, λ) designs with λ 2.

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DO - 10.1093/qmath/haw001

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JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

IS - 1

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Generating groups using hypergraphs

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