AbstractLet h ≥ 2 be any integer, let c = h(1 + 2−1h)h − 1. In this paper, it is proved that every finite abelian group G contains a subset A such that hA = G and |A| ≤ c |G|1h, where hA denotes the set of all sums of h not necessarily distinct elements in A, and |A| denotes the cardinality of the set A
AbstractThe following theorem is proved. If a1, … ak are distinct elements of a group, written addit...
Abstract. Let G be an infinite abelian group with |2G | = |G|. We show that if G is not the direct ...
AbstractLet G≃Z/k1Z⊕⋯⊕Z/kNZ be a finite abelian group with ki|ki−1(2≤i≤N). For a matrix Y=(ai,j)∈ZR×...
AbstractIn this paper, it is proved that for every h ≥ 2, every finite nilpotent group G of order n ...
AbstractLet G be a multiplicative group, and let h ≥ 2. Let B be a subset of G. Denote by Bh the set...
Let $G$ be a finite abelian group and $s$ be a positive integer. A subset $A$ of $G$ is called a {\e...
AbstractLet G be a group written additively and let A denote a set of nonzero elements of G. The sma...
Let $G$ be a finite abelian group. A nonempty subset $A$ in $G$ is called a basis of order $h$ if $h...
For a non-empty $k$-element set $A$ of an additive abelian group $G$ and a positive integer $r \leq ...
AbstractA subset X of an abelian G is said to be complete if every element of G can be expressed as ...
AbstractIf G is a finite Abelian group, for what number s is it true that an arbitrary sequence of l...
AbstractWe establish several addition theorems on finite abelian groups by employing a group ring as...
Let B be a proper subset of a finite group G such that either B = B−1 or G is abelian. We prove that...
AbstractIn this paper we investigate the set of all sums over subsequences of a sequence a1,…, as of...
AbstractLetGbe an abelian group containing a finite subsetBsuch that, for every non-empty finite sub...
AbstractThe following theorem is proved. If a1, … ak are distinct elements of a group, written addit...
Abstract. Let G be an infinite abelian group with |2G | = |G|. We show that if G is not the direct ...
AbstractLet G≃Z/k1Z⊕⋯⊕Z/kNZ be a finite abelian group with ki|ki−1(2≤i≤N). For a matrix Y=(ai,j)∈ZR×...
AbstractIn this paper, it is proved that for every h ≥ 2, every finite nilpotent group G of order n ...
AbstractLet G be a multiplicative group, and let h ≥ 2. Let B be a subset of G. Denote by Bh the set...
Let $G$ be a finite abelian group and $s$ be a positive integer. A subset $A$ of $G$ is called a {\e...
AbstractLet G be a group written additively and let A denote a set of nonzero elements of G. The sma...
Let $G$ be a finite abelian group. A nonempty subset $A$ in $G$ is called a basis of order $h$ if $h...
For a non-empty $k$-element set $A$ of an additive abelian group $G$ and a positive integer $r \leq ...
AbstractA subset X of an abelian G is said to be complete if every element of G can be expressed as ...
AbstractIf G is a finite Abelian group, for what number s is it true that an arbitrary sequence of l...
AbstractWe establish several addition theorems on finite abelian groups by employing a group ring as...
Let B be a proper subset of a finite group G such that either B = B−1 or G is abelian. We prove that...
AbstractIn this paper we investigate the set of all sums over subsequences of a sequence a1,…, as of...
AbstractLetGbe an abelian group containing a finite subsetBsuch that, for every non-empty finite sub...
AbstractThe following theorem is proved. If a1, … ak are distinct elements of a group, written addit...
Abstract. Let G be an infinite abelian group with |2G | = |G|. We show that if G is not the direct ...
AbstractLet G≃Z/k1Z⊕⋯⊕Z/kNZ be a finite abelian group with ki|ki−1(2≤i≤N). For a matrix Y=(ai,j)∈ZR×...
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