منابع مشابه
Constructing Free Groups in Quaternion Algebras
In [4] it was shown for a suitable power n of a pair of units u, v of the quaternions algebras over the ring of integers of imaginary rational extensions A = H(o Q √ −d ) that the group generated by u, v is a free group in the unit group of A when d ≡ 7 (mod 8) is a positive square free integer. We extend this result for any imaginary rational extension and show that the group generated by u, v...
متن کاملHyperbolic Unit Groups and Quaternion Algebras
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 [...
متن کاملSchur Indices in Finite Quaternion-free Groups
Let G be a finite, quaternion-free group with exponent e, let F be a field of characteristic zero and let x be an absolutely irreducible character of G. Suppose that a Sylow 2-subgroup of the Galois group of F(J\) over F is cyclic. It is shown that if x is not real valued, then the Schur index of x over F is odd. Let G be a finite group with exponent e and let F be a field of characteristic zer...
متن کاملQuaternion Algebras, Arithmetic Kleinian Groups and Z-lattices
Let K be a quadratic extension of Q, B a quaternion algebra over Q and A = B ⊗Q K. Let O be a maximal order in A extending an order in B. The projective norm one group PO1 is shown to be isomorphic to the spinorial kernel group O′(L), for an explicitly determined quadratic Z-lattice L of rank four, in several general situations. In other cases, only the local structures of O and L are given at ...
متن کاملQuaternion Algebras
The additive identity is (0, 0), the multiplicative identity is (1, 0), and from addition and scalar multiplication of real vectors we have (a, b) = (a, 0) + (0, b) = a(1, 0) + b(0, 1), which looks like a+ bi if we define i to be (0, 1). Real numbers occur as the pairs (a, 0). Hamilton asked himself if it was possible to multiply triples (a, b, c) in a nice way that extends multiplication of co...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2013
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2012.12.025