A representation theorem for abelian groups with no elements of infinitep-height
نویسندگان
چکیده
منابع مشابه
non-divisibility for abelian groups
Throughout all groups are abelian. We say a group G is n-divisible if nG = G. If G has no non-zero n-divisible subgroups for all n>1 then we say that G is absolutely non-divisible. In the study of class C consisting all absolutely non-divisible groups such as G, we come across the sub groups T_p(G) = the sum of all p-divisible subgroups and rad_p(G) = the intersection of all p^nG. The proper...
متن کاملHindman’s Theorem in Abelian Groups
Hindman’s theorem tells us that for every finite colouring/partition of the natural numbers, there is an infinite subset X for which every finite subset X0 Ď X has the same colour for ř X0. Certain generalisations of this theorem to abelian groups are known to fail in the uncountable case but an example exists for boolean groups when the desired homogeneous set is finite. In this paper, I will ...
متن کاملDecomposition of Elements in Abelian Groups*
In the present paper we determine necessary and sufficient conditions for an abelian group to have the property Pw . The author first proved the validity of these conditions for fields, but, as noted by T. Nakayama, the operation X does not occur, so that the theory may be stated for a system of elements with only one operation + defined for these elements. Groups with the property Pn have usef...
متن کاملGenerating random elements of abelian groups
Algorithms based on rapidly mixing Markov chains are discussed to produce nearly uniformly distributed random elements in abelian groups of finite order. Let A be an abelian group generated by set S. Then one can generate ε-nearly uniform random elements of A using 4|S| log(|A| /ε) log(|A|) additions and the same number of random bits.
متن کاملA representation for some groups, a geometric approach
In the present paper, we are going to use geometric and topological concepts, entities and properties of the integral curves of linear vector fields, and the theory of differential equations, to establish a representation for some groups on $R^{n} (ngeq 1)$. Among other things, we investigate the surjectivity and faithfulness of the representation. At the end, we give some app...
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: Pacific Journal of Mathematics
سال: 1967
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1967.20.31