CORE
πΊπ¦Β
Β make metadata, not war
Services
Services overview
Explore all CORE services
Access to raw data
API
Dataset
FastSync
Content discovery
Recommender
Discovery
OAI identifiers
OAI Resolver
Managing content
Dashboard
Bespoke contracts
Consultancy services
Support us
Support us
Membership
Sponsorship
Community governance
Advisory Board
Board of supporters
Research network
About
About us
Our mission
Team
Blog
FAQs
Contact us
research
Conway groupoids, regular two-graphs and supersimple designs
Authors
Nick Gill
Neil I. Gillespie
Cheryl E. Praeger
Jason Semeraro
Publication date
22 October 2015
Publisher
View
on
arXiv
Abstract
A
2
β
(
n
,
4
,
Ξ»
)
2-(n,4,\lambda)
2
β
(
n
,
4
,
Ξ»
)
design
(
Ξ©
,
B
)
(\Omega, \mathcal{B})
(
Ξ©
,
B
)
is said to be supersimple if distinct lines intersect in at most two points. From such a design, one can construct a certain subset of Sym
(
Ξ©
)
(\Omega)
(
Ξ©
)
called a "Conway groupoid". The construction generalizes Conway's construction of the groupoid
M
13
M_{13}
M
13
β
. It turns out that several infinite families of groupoids arise in this way, some associated with 3-transposition groups, which have two additional properties. Firstly the set of collinear point-triples forms a regular two-graph, and secondly the symmetric difference of two intersecting lines is again a line. In this paper, we show each of these properties corresponds to a group-theoretic property on the groupoid and we classify the Conway groupoids and the supersimple designs for which both of these two additional properties hold.Comment: 17 page
Similar works
Full text
Open in the Core reader
Download PDF
Available Versions
Supporting member
Explore Bristol Research
See this paper in CORE
Go to the repository landing page
Download from data provider
oai:research-information.bris....
Last time updated on 24/02/2017