TY - JOUR
T1 - On a class of affine geometries
AU - Hoffman, C.
AU - Parker, C.W.
AU - Shpectorov, S.
N1 - Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2012/9/1
Y1 - 2012/9/1
N2 - The far-away geometry ∑ in a symplectic polar space is the subgeometry on the points non-collinear to a fixed point. In case of the polar space of rank three we define a class of subgeometries of ∑ with the same points and lines as ∑ and some of the planes of ∑ removed. We show that such geometries are simply connected, unless ∑ is defined over GF(2). As an application, for a particular such subgeometry Γ we exhibit a flag-transitive group G and, as a result, we get an amalgam presentation for this G. The smallest instance (over GF(3)) of G is related to the sporadic Thompson simple group.
AB - The far-away geometry ∑ in a symplectic polar space is the subgeometry on the points non-collinear to a fixed point. In case of the polar space of rank three we define a class of subgeometries of ∑ with the same points and lines as ∑ and some of the planes of ∑ removed. We show that such geometries are simply connected, unless ∑ is defined over GF(2). As an application, for a particular such subgeometry Γ we exhibit a flag-transitive group G and, as a result, we get an amalgam presentation for this G. The smallest instance (over GF(3)) of G is related to the sporadic Thompson simple group.
UR - http://www.scopus.com/inward/record.url?partnerID=yv4JPVwI&eid=2-s2.0-84870221294&md5=2d82e65213ce5f34d5e6cedb525fa694
U2 - 10.1515/advgeom-2012-0015
DO - 10.1515/advgeom-2012-0015
M3 - Article
AN - SCOPUS:84870221294
SN - 1615-715X
VL - 12
SP - 381
EP - 399
JO - Advances in Geometry
JF - Advances in Geometry
IS - 3
ER -