Hyperbolic Unit Groups and Quaternion Algebras
نویسندگان
چکیده
We classify the quadratic extensions K = Q[ √ d] and the finite groups G for which the group ring oK [G] of G over the ring oK of integers of K has the property that the group U1(oK [G]) of units of augmentation 1 is hyperbolic. We also construct units in the Z-order H(oK) of the quaternion algebra H(K) = ` −1, −1 K ́ , when it is a division algebra. Mathematics Subject Classification. Primary [16U60]. Secondary [16S34, 20F67] [keywords] Hyperbolic Groups, Quaternion Algebras, Free Groups, Group Rings, Units
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