TY - JOUR

T1 - Generating groups using hypergraphs

AU - Gill, Nick

AU - Gillespie, Neil

AU - Nixon, Anthony Keith

AU - Semeraro, Jason

N1 - This is a pre-copy-editing, author-produced PDF of an article accepted for publication in The Quarterly Journal of Mathematics following peer review. The definitive publisher-authenticated version Nick Gill, Neil I. Gillespie, Anthony Nixon, and Jason Semeraro GENERATING GROUPS USING HYPERGRAPHS Q J Math (2016) 67 (1): 29-52 doi:10.1093/qmath/haw001 is available online at: http://qjmath.oxfordjournals.org/content/67/1/29.abstract

PY - 2016/3/7

Y1 - 2016/3/7

N2 - To a set $\B$ of 4-subsets of a set $\Omega$ of size $n$ we introduce an invariant called the `hole stabilizer' which generalises a construction of Conway, Elkies and Martin of the Mathieu group $M_{12}$ based on Loyd'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 $(\Omega,\B)$ with a trivial hole stabilizer, and determine all hole stabilizers associated to $2$-$(n,4,\lambda)$ designs with $\lambda \leq 2$.

AB - To a set $\B$ of 4-subsets of a set $\Omega$ of size $n$ we introduce an invariant called the `hole stabilizer' which generalises a construction of Conway, Elkies and Martin of the Mathieu group $M_{12}$ based on Loyd'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 $(\Omega,\B)$ with a trivial hole stabilizer, and determine all hole stabilizers associated to $2$-$(n,4,\lambda)$ designs with $\lambda \leq 2$.

U2 - 10.1093/qmath/haw001

DO - 10.1093/qmath/haw001

M3 - Journal article

VL - 67

SP - 29

EP - 52

JO - The Quarterly Journal of Mathematics

JF - The Quarterly Journal of Mathematics

SN - 0033-5606

IS - 1

ER -