On relative position in extensions of combinatorial geometries
نویسندگان
چکیده
منابع مشابه
9 Combinatorial Geometries of Field Extensions
We classify the algebraic combinatorial geometries of arbitrary field extensions of transcendence degree greater than 4 and describe their groups of automorphisms. Our results and proofs extend similar results and proofs by Evans and Hrushovski in the case of algebraically closed fields. The classification of projective planes in algebraic combinatorial geometries in arbitrary fields of charact...
متن کاملCombinatorial Geometries of the Field Extensions
We classify projective planes in algebraic combinatorial geometries in arbitrary fields of characteristic zero. We investigate the first-order theories of such geometries and pregeometries. Then we classify the algebraic combinatorial geometries of arbitrary field extensions of the transcendence degree ≥ 5 and describe their groups of automorphisms. Our results and proofs extend similar results...
متن کاملON RELATIVE CENTRAL EXTENSIONS AND COVERING PAIRS
Let (G;N) be a pair of groups. In this article, first we con-struct a relative central extension for the pair (G;N) such that specialtypes of covering pair of (G;N) are homomorphic image of it. Second, weshow that every perfect pair admits at least one covering pair. Finally,among extending some properties of perfect groups to perfect pairs, wecharacterize covering pairs of a perfect pair (G;N)...
متن کاملVarieties of Combinatorial Geometries
A hereditary class of (finite combinatorial) geometries is a collection of geometries which is closed under taking minors and direct sums. A sequence of universal models for a hereditary class 'S of geometries is a sequence (T„ ) of geometries in ?T with rank Tn = n, and satisfying the universal property: if G is a geometry in 5" of rank n, then G is a subgeometry of T„. A variety of geometries...
متن کامل1.1. Combinatorial Geometries 3
Quasiminimality In this chapter we introduce Zilber’s notion [Zil05] of an abstract quasiminimalexcellent class and prove Theorem 2.23: Lω1,ω-definable quasiminimal-excellent classes satisfying the countable closure condition are categorical in all powers. In the next chapter we expound Zilber’s simplest concrete algebraic example. In Chapter 25, we will place this example in the context of She...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1988
ISSN: 0095-8956
DOI: 10.1016/0095-8956(88)90088-3