ellipse rotating symmetric group is proposed, which is an Abelian group.───提出椭圆旋转对称群,它是一个单参数阿贝尔群。 Let Г be anabelian group.───设Г是交换群. 英语使用场景 Some conditions were discussed, under which a group become anabelian group. ...
A. M. Sebel'din, “Determinability of an unreduced torsion-free Abelian group by its group of endomorphisms,” in: “Abelian groups and modules,” Tomsk (1980), p. 102–108. N. A. Serdyukova, “Classes of Abelian groupsG satisfying the conditionst p Ext(Z ω α, G= 0,” Moscow...
An Abelian group (in additive notation) is a triple2〈A, +, 0〉 consisting of a set A, a binary operation + on A, and an element (“zero“) of A, such that the following conditions are met: 1. + is associative and commutative. 2. 0 is an identity element, i.e., x + 0 ...
New necessary conditions for Paley type partial difference sets in Abelian groupsPaley partial difference setpartial difference setstrongly regular graphIn this paper we prove that if there is a regular Paley type partial difference set in an Abelian group G of order v, where v = p21k1p22k2 *...
In a locally compact abelian p-group G the following conditions are equivalent: (1) G is neat. (2) For every finitely generated subgroup H of G there is a finitely generated direct summand P of G such that H\le P and that \textrm{rank}_p(H)=\textrm{rank}_p(P). Proof (2)...
Let G be a finitely generated abelian group. Then (1) G≅Zr×Zn1×Zn2×⋯Zns, for some r, n1, r2, ⋯, ns∈N satisfying the following conditions: (a) r≥0 and nj≥2, ∀j; (b) ni+1∣ni, for 1≤i≤s−1. (2) the expression in (1) is unique. Definition 3. The...
For a positive integer k, let f(k) denote the largest integer t such that for every finite abelian group G and every zero-sum free subset S of G, if |S|=k then |Σ(S)|≥t. In this paper, we prove that f(k)≥16k2, which significantly improves a result of J.E. Olson. We...
Let's consider the following Abelian Group: The set of elements is the set of integers. The binary operation is the numeric addition. The identity element is the integer 0. You can verify that all 5 Abelian Group conditions are satisfied. For example: ...
For a finite abelian p-group A of type (k 1, ..., k n), simple necessary and sufficient conditions for an n × n-matrix over integers to be associated with an automorphism of A are presented. Then, the automorphism group Aut(A) for a finite p-group A of type (k 1, k 2) is...
Skew group ringsSimplicityTransformation groupsNecessary and sufficient conditions for simplicity of a general skew group ring A G are not known. In this article, we show that a skew group ring A G, of an abelian group G, is simple if and only if its centre is a field and A is G-...