Geodesic
Net determinant over a Bezoutian local ring
Zapiski Nauchnykh Seminarov POMI, Integral lattices and finite linear groups, Tome 116 (1982), pp. 5-13 
Z. I. Borevich; N. A. Vavilov. Net determinant over a Bezoutian local ring. Zapiski Nauchnykh Seminarov POMI, Integral lattices and finite linear groups, Tome 116 (1982), pp. 5-13. http://geodesic.mathdoc.fr/item/ZNSL_1982_116_a0/
@article{ZNSL_1982_116_a0,
     author = {Z. I. Borevich and N. A. Vavilov},
     title = {Net determinant over a {Bezoutian} local ring},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--13},
     year = {1982},
     volume = {116},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_116_a0/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $\sigma$ be any $D$-net of ideals of order $n$ over a commutative local Bezoutian ring $R$ and denote by $G(\sigma)$ the corresponding net subgroup in the general linear group of degree $n$ over $R$ (RZhMat, 1977, 2A280). We give an explicit computation of the factor group $G(\sigma)/E(\sigma)$, where $E(\sigma)$ is the subgroup generated by all elementary transvections in $G(\sigma)$.