Geodesic
Isometries of semi-orthogonal forms on a~$\mathbb Z$-module of rank~3
Izvestiya. Mathematics , Tome 77 (2013) no. 1, pp. 44-86

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We study the isometry groups of semi-orthogonal forms (that is, forms whose Gram matrix in some basis is upper triangular with ones on the diagonal) on a $\mathbb Z$-module of rank 3. Such forms have a discrete parameter: the height (the trace of the dualizing operator + 3). We prove that the isometry group is either $\mathbb Z$ or $\mathbb Z_2\times\mathbb Z$, list all the cases when it is a direct product and describe the generator of order 2 in that case. We also describe a generator of infinite order for many particular values of the height.
Keywords: quadratic forms on modules over rings. 
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     title = {Isometries of semi-orthogonal forms on a~$\mathbb Z$-module of rank~3},
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S. A. Kuleshov. Isometries of semi-orthogonal forms on a~$\mathbb Z$-module of rank~3. Izvestiya. Mathematics , Tome 77 (2013) no. 1, pp. 44-86. http://geodesic.mathdoc.fr/item/IM2_2013_77_1_a4/