Algebraic (2,2)-transformation groups

Details Algebraic (2,2)-transformation groups Algebraic (2,2)-transformation groups

2008-09-25

arxiv.org/abs/0809.4443v1

Mathematics

Group Theory

11 pages, this paper contains the more significant part of the article with the same title that will appear in the Volume 12 o

Scientific paper

This paper contains the more significant part of the article with the same title that will appear in the Volume 12 of Journal of Group Theory (2009). In this paper we determine all algebraic transformation groups $G$, defined over an algebraically closed field $\sf k$, which operate transitively, but not primitively, on a variety $\Omega$, provided the following conditions are fulfilled. We ask that the (non-effective) action of $G$ on the variety of blocks is sharply 2-transitive, as well as the action on a block $\Delta$ of the normalizer $G_\Delta$. Also we require sharp transitivity on pairs $(X,Y)$ of independent points of $\Omega$, i.e. points contained in different blocks.

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