On Presentations of Integer Polynomial Points of Simple Groups over Number Fields
نویسندگان
چکیده
0.1. Related results. Krstić-McCool proved that GL3(A) is not finitely presented if there is an epimorphism from A to F [t] for some field F [Krs-Mc]. Suslin proved that SLn(A[t1, . . . , tk]) is generated by elemetary matrices if n ≥ 3, A is a regular ring, and K1(A) ∼= A× [Su]. GrunewaldMennicke-Vaserstein proved that Sp2n(A[t1, . . . , tk]) is generated by elementary matrices if n ≥ 2 and A is a Euclidean ring or a local principal ideal ring [G-M-V]. In Bux-Mohammadi-Wortman, it’s shown that SLn(Z[t]) is not of type FPn−1 [B-M-W]. The case when n = 3 is a special case of Theorem 1. While most of the results listed above allow for more general rings than OK [t], the result of this paper, and the techniques used to prove it, are distinguished by their applicability to a class of semisimple groups that extends beyond special linear and symplectic groups.
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