Geodesic
Partial geometries $\bold{pg}(s,t,\bold 2$) with an abelian Singer group and a characterization of the van Lint-Schrijver partial geometry
Journal of Algebraic Combinatorics, Tome 24 (2006) no. 3, pp. 285-297.

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Summary: Let $S$ mathcalS be a proper partial geometry $pg( s, t,2)$, and let $G$ be an abelian group of automorphisms of $S$ mathcalS acting regularly on the points of $S$ mathcalS. Then either $t\equiv 2\pm od s+1$ or $S$ mathcalS is a $pg(5,5,2)$ isomorphic to the partial geometry of van Lint and Schrijver (Combinatorica 1 (1981), 63-73). This result is a new step towards the classification of partial geometries with an abelian Singer group and further provides an interesting characterization of the geometry of van Lint and Schrijver.
Keywords: keywords partial geometry, abelian singer group, geometry of Van lint-schrijver 
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     author = {De Winter, S.},
     title = {Partial geometries $\bold{pg}(s,t,\bold 2$) with an abelian {Singer} group and a characterization of the van {Lint-Schrijver} partial geometry},
     journal = {Journal of Algebraic Combinatorics},
     pages = {285--297},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2006__24_3_a3/}
}
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De Winter, S. Partial geometries $\bold{pg}(s,t,\bold 2$) with an abelian Singer group and a characterization of the van Lint-Schrijver partial geometry. Journal of Algebraic Combinatorics, Tome 24 (2006) no. 3, pp. 285-297. http://geodesic.mathdoc.fr/item/JAC_2006__24_3_a3/