Detecting products of elementary matrices in

Author:
Randy Tuler

Journal:
Proc. Amer. Math. Soc. **89** (1983), 45-48

MSC:
Primary 10C30; Secondary 10C02, 10M20, 15A23, 20H25

MathSciNet review:
706508

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Abstract: An elementary matrix over a ring has 1 in each diagonal position and at most one additional nonzero element. Let where is an integer less than . We give an algorithm for determining whether or not a invertible matrix over is generated by elementary matrices. This is connected with the theory of integral binary quadratic forms.

**[1]**P. M. Cohn,*On the structure of the 𝐺𝐿₂ of a ring*, Inst. Hautes Études Sci. Publ. Math.**30**(1966), 5–53. MR**0207856****[2]**Burton W. Jones,*The Arithmetic Theory of Quadratic Forms*, Carcus Monograph Series, no. 10, The Mathematical Association of America, Buffalo, N. Y., 1950. MR**0037321****[3]**Robert Riley,*Applications of a computer implementation of Poincaré’s theorem on fundamental polyhedra*, Math. Comp.**40**(1983), no. 162, 607–632. MR**689477**, 10.1090/S0025-5718-1983-0689477-2**[4]**Richard G. Swan,*Generators and relations for certain special linear groups*, Advances in Math.**6**(1971), 1–77 (1971). MR**0284516****[5]**Randy Tuler,*Subgroups of 𝑆𝐿₂𝑍 generated by elementary matrices*, Proc. Roy. Soc. Edinburgh Sect. A**88**(1981), no. 1-2, 43–47. MR**611299**, 10.1017/S0308210500017273

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DOI:
https://doi.org/10.1090/S0002-9939-1983-0706508-3

Article copyright:
© Copyright 1983
American Mathematical Society