We study Aat flag-transitive c.c*-geometries. We prove that, apart from one exception related to Sym(6), all these geometries are gluings in the meaning of [6]. They are obtained by gluing two copies of an affine space over GF(2). There are several ways of gluing two copies of the n-dimensional affine space over GF(2). In one way, which deserves to be called the canonical one, we get a geometry with automorphism group G = 2(2n) . L(n)(2) and covered by the truncated Coxeter complex of type D-2n. The non-canonical ways give us geometries with smaller automorphism group (G less than or equal to 2(2n) . (2(n)-1)(n)) and which seldom (never ?) can be obtained as quotients of truncated Coxeter complexes.

Baumeister, B., & Pasini, A. (1997). Ob flat flag-transitive c.c*-geometries. JOURNAL OF ALGEBRAIC COMBINATORICS, 6(1), 5-26.

Ob flat flag-transitive c.c*-geometries

PASINI, ANTONIO
1997

Abstract

We study Aat flag-transitive c.c*-geometries. We prove that, apart from one exception related to Sym(6), all these geometries are gluings in the meaning of [6]. They are obtained by gluing two copies of an affine space over GF(2). There are several ways of gluing two copies of the n-dimensional affine space over GF(2). In one way, which deserves to be called the canonical one, we get a geometry with automorphism group G = 2(2n) . L(n)(2) and covered by the truncated Coxeter complex of type D-2n. The non-canonical ways give us geometries with smaller automorphism group (G less than or equal to 2(2n) . (2(n)-1)(n)) and which seldom (never ?) can be obtained as quotients of truncated Coxeter complexes.
Baumeister, B., & Pasini, A. (1997). Ob flat flag-transitive c.c*-geometries. JOURNAL OF ALGEBRAIC COMBINATORICS, 6(1), 5-26.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/7080
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