6533b7d8fe1ef96bd126b71f
RESEARCH PRODUCT
Algebraic (2, 2)-transformation groups
Claudio BartoloneAlfonso Di BartoloKarl Strambachsubject
Transitive relationAlgebra and Number TheoryNaturwissenschaftliche Fakultät -ohne weitere Spezifikation-14L30permutation groupsBlock (permutation group theory)-Group Theory (math.GR)Permutation groupCentralizer and normalizerAction (physics)CombinatoricsFOS: Mathematicsddc:510Variety (universal algebra)Algebraically closed fieldAlgebraic numberMathematics - Group TheoryMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2009-01-01 | Journal of Group Theory |