Given a set of types I. a type 0 is an element of I, a subset J of I containing 0, and a diagram I(0) over I{0}. a geometry Gamma over the set of types J is said to be locally truncated of I(0)-type if the J{0}-residues of Gamma are truncations of geometries or chamber systems belonging to I(0). We give a sufficent condition for such a geometry to be the J-truncation of a chamber system over the set of types I with all I{0}-residues belonging to I(0). Then we apply our result to some special cases. We exploit it to classify flag-transitive c(n),c*-geometries of rank n + 2 greater than or equal to 4 and c(n),c*-geometries of order 2. We give a new proof of a theorem of Ronan on C(n),L-geometries and we construct chamber systems for a number of sporadic groups in which certain well known geometries are involved as truncations or residues. (C) 2001 Academic Press.
Ceccherini, G., Pasini, A. (2001). Extending locally truncated geometries. JOURNAL OF COMBINATORIAL THEORY. SERIES A, 94(2), 289-338 [10.1006/jcta.2000.3138].
Extending locally truncated geometries
PASINI, ANTONIO
2001-01-01
Abstract
Given a set of types I. a type 0 is an element of I, a subset J of I containing 0, and a diagram I(0) over I{0}. a geometry Gamma over the set of types J is said to be locally truncated of I(0)-type if the J{0}-residues of Gamma are truncations of geometries or chamber systems belonging to I(0). We give a sufficent condition for such a geometry to be the J-truncation of a chamber system over the set of types I with all I{0}-residues belonging to I(0). Then we apply our result to some special cases. We exploit it to classify flag-transitive c(n),c*-geometries of rank n + 2 greater than or equal to 4 and c(n),c*-geometries of order 2. We give a new proof of a theorem of Ronan on C(n),L-geometries and we construct chamber systems for a number of sporadic groups in which certain well known geometries are involved as truncations or residues. (C) 2001 Academic Press.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/11365/17589
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