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Modular group gamma sibling?

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Mikito Harakiri

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Jul 17, 2004, 1:33:42 AM7/17/04
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I'm studying semigroup that is generated by multiplication of 2x2
matrixes like this:

N=Matrix(2,2,[[n,1],[1,0]])

where n integer >=1. Unlike modular group gamma the decomposition of
any element

Matrix(2,2,[[a,b],[c,d]])=N_1.N_2.N_3...N_k

is always unique. The other distinction is that the determinant is
always either 1 or -1. What is the name of this subgroup?

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