Direct sums and products of isomorphic abelian groups
نویسندگان
چکیده
منابع مشابه
Direct Products of Ordered Abelian Groups
In this paper we study some theories of direct products of ordered abelian
متن کامل16A. Direct products and Classification of Finite Abelian Groups
Definition. Let G and H be groups. Their direct product is the group G×H defined as follows. As a set G×H = {(g, h) : g ∈ G, h ∈ H} is just the usual Cartesian product of G and H (the set of ordered pairs where the first component lies in G and the second component lies in H). The group operation on G×H is defined by the formula (g1, h1)(g2, h2) = (g1g2, h1h2) for all g1, g2 ∈ G and h1, h2 ∈ H....
متن کاملBracket Products on Locally Compact Abelian Groups
We define a new function-valued inner product on L2(G), called ?-bracket product, where G is a locally compact abelian group and ? is a topological isomorphism on G. We investigate the notion of ?-orthogonality, Bessel's Inequality and ?-orthonormal bases with respect to this inner product on L2(G).
متن کاملk-Sums in Abelian Groups
Given a finite subset A of an abelian group G, we study the set k ∧ A of all sums of k distinct elements of A. In this paper, we prove that |k ∧A| > |A| for all k ∈ {2, . . . , |A| − 2}, unless k ∈ {2, |A| − 2} and A is a coset of an elementary 2-subgroup of G. Furthermore, we characterize those finite sets A ⊆ G for which |k ∧ A| = |A| for some k ∈ {2, . . . , |A| − 2}. This result answers a q...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1987
ISSN: 0035-7596
DOI: 10.1216/rmj-1987-17-3-573