By A. Bak

**Read Online or Download Algebraic K-theory, number theory, geometry, and analysis: proceedings of the international conference held at Bielefeld, Federal Republic of Germany, July 26-30, 1982 PDF**

**Similar geometry and topology books**

- Beitrag zur Optimierung der Spitzengeometrie von Spiralbohrern mil Hilfe des genetischen Algorilhmus
- The elements of non-Euclidean geometry
- Problems in Geometry
- Éléments de Mathématique: Integration -6. Chapitre 6
- Dimension and Extensions
- Geometrical Combinatorial Topology: v. 2

**Additional resources for Algebraic K-theory, number theory, geometry, and analysis: proceedings of the international conference held at Bielefeld, Federal Republic of Germany, July 26-30, 1982**

**Sample text**

Ut+i}. We may suppose that m < t + 1. For % > m, let Li be the line xut and let M, be the line yui. Let K be the line incident with z and concurrent with Liy and let AT be the line incident with z and concurrent with Mj. Let M be the line incident with y and concurrent with K, and let L be the line incident with x and concurrent with N. Since the line Li is regular, the pair {Li, N} must be regular, and it follows that M must meet L in some point m> e {x, y}- 1 , m + 1 < i' < t + 1, i' 7^ i. In this way with each point Ui e {u m + 1 , u m + 2 , .

3) Suppose G is as in (3) of the statement. Suppose x e V Xp1- is a point for which \GX \ ^ 1. Then G is a Frobenius group in its action on the G-orbit X of x. So the Frobenius kernel TV of G acts sharply transitively on X. As G is generated by elations about p, G itself acts sharply transitively on X. It follows that G is a group of elations about p. (4) This follows from (3). (5) This follows immediately from (3). 2 • 4-Gonal Families and EGQs In this section it is explained how EGQs can always be represented as a group coset geometry, and vice versa.

4 Let S be a GQ of order s, s ^ 1, having an antiregular point x. Then S = Q(4, s) if and only if there is a point y, with y e a;-L\{a;}, for which the affine plane ir(x, y) is Desarguesian. Proof. 7 of Payne and Thas [128]. 4 is equivalent to saying that a Laguerre plane £ of odd order s is classical if and only if at least one of the internal planes £y is Desarguesian. We end this section with a remarkable theorem due to Bagchi, Brouwer and Wilbrink [6], the proof of which is entirely in terms of codes.