Geodesic
Tactical decompositions of Steiner systems and orbits of projective groups
Journal of Algebraic Combinatorics, Tome 12 (2000) no. 2, pp. 123-130.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Block's lemma states that the numbers $m$ of point-classes and $n$ of block-classes in a tactical decomposition of a 2-( $v, k, lambda$) design with $b$ blocks satisfy $mlenlem + b - v$. We present a strengthening of the upper bound for the case of Steiner systems (2-designs with $lambda$ = 1), together with results concerning the structure of the block-classes in both extreme cases. Applying the results to the Steiner systems of points and lines of projective space $PG( N, q)$, we obtain a complete classification of the groups inducing decompositions satisfying the upper bound; answering the analog of a question raised by Cameron and Liebler (P.J. Cameron and R.A. Liebler, Lin. Alg. Appl. 46 (1982), 91-102) (and still open).
Keywords: tactical decompositions, partial spread, tightset, Steiner systems, projective group 
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     author = {Drudge, Keldon},
     title = {Tactical decompositions of {Steiner} systems and orbits of projective groups},
     journal = {Journal of Algebraic Combinatorics},
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Drudge, Keldon. Tactical decompositions of Steiner systems and orbits of projective groups. Journal of Algebraic Combinatorics, Tome 12 (2000) no. 2, pp. 123-130. http://geodesic.mathdoc.fr/item/JAC_2000__12_2_a4/