Geodesic
Finite Projective Planes that Admit a Strongly Irreducible Collineation Group
Canadian journal of mathematics, Tome 37 (1985) no. 4, pp. 579-611

Voir la notice de l'article provenant de la source Cambridge University Press

This paper studies how coding theory and group theory can be used to produce information about a finite projective plane π and a collineation group G of π.A new proof for Hering's bound on |G| is given in 2.5. Using the idea of coding theory developed in [9], a relation between two rows of the incidence matrix of π with respect to a tactical decomposition is obtained in 2.1. This result yields, among other things, some techniques in calculating |G|, and generalizes a result of Roth [16], [see 2.4 and 2.5].Hering [7] introduced the notion of strong irreducibility of G, that is, G does not leave invariant any point, line, triangle or proper subplane. He showed that if in addition G contains a non-trivial perspectivity, then there is a unique minimal normal subgroup of G. This subgroup is either non-abelian simple or isomorphic to the elementary abelian group Z 3 × Z 3 of order 9. 
Ho, Chat Yin. Finite Projective Planes that Admit a Strongly Irreducible Collineation Group. Canadian journal of mathematics, Tome 37 (1985) no. 4, pp. 579-611. doi: 10.4153/CJM-1985-031-8
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