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...
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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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The level of a ring R with 1 6= 0 is the smallest positive integer s such that −1 can be written as a sum of s squares in R, provided −1 is a sum of squares at all. D.W. Lewis showed that any value of type 2n or 2n + 1 can be realized as level of a quaternion algebra, and he asked whether there exist quaternion algebras whose levels are not of that form. Using function fields of quadratic forms...
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In this paper we define S algebras and show that every finite group can be found in some S algebra. We define and study the S degree of a finite group and determine the S degree of several classes of finite groups such as cyclic groups, elementary abelian $p$-groups, and dihedral groups $D_p$.
متن کاملSelectivity in Quaternion Algebras
Let A be a quaternion algebra over a number field K and assume that A satisfies the Eichler condition; that is, there exists an archimedean prime of K which does not ramify in A. Let Ω be a commutative, quadratic OK-order and let R ⊂ A be an order. We determine the isomorphism classes in the genus of R which admit an embedding of Ω. In particular, we show that the proportion of the genus of R a...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1993
ISSN: 0002-9939
DOI: 10.2307/2160003