#### Vol. 12, No. 1, 2011

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### William Cherowitzo and Norman L. Johnson

Vol. 12 (2011), No. 1, 21–34
##### Abstract

In this article, it is shown that every flock of a hyperbolic quadric $H$ and every flock of a quadratic cone $C$ in $PG\left(3,K\right)$, for $K$ a field, is in a transitive parallelism of $H$ or $C$, respectively. Furthermore, it is shown it is possible to have parallelisms of quadratic cones by maximal partial flocks. The theory of parallelisms of quadratic cones is generalized to analogous results for parallelisms of $\alpha$-cones.

##### Keywords
flocks, flokki, parallelisms, hyperbolic quadric, elliptic quadric, quadratic cone, $\alpha$-cone
##### Mathematical Subject Classification 2010
Primary: 51A15, 51E20