Geodesic
Two-Dimensional Linear Groups Over Local Rings
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 106-135

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

The problem of classifying the normal subgroups of the general linear group over a field was solved in the general case by Dieudonné (see 2 and 3). If we consider the problem over a ring, it is trivial to see that there will be more normal subgroups than in the field case. Klingenberg (4) has investigated the situation over a local ring and has shown that they are classified by certain congruence groups which are determined by the ideals in the ring.Klingenberg's solution roughly goes as follows. To a given ideal , attach certain congruence groups and . Next, assign a certain ideal (called the order) to a given subgroup G. The main result states that if G is normal with order a, then ≧ G ≧ , that is, G satisfies the so-called ladder relation at ; conversely, if G satisfies the ladder relation at , then G is normal and has order . 
Lacroix, Norbert H. J. Two-Dimensional Linear Groups Over Local Rings. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 106-135. doi: 10.4153/CJM-1969-011-8
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