It was proved by Banakh and Protasov that every group can be generated by a small set (in the sense of Malykhin and Bella). The paper strenghtens this result be replacing "small set" by "P-small subset" (these are sets that have infinitely many pairwise disjoint left translates)
AbstractLet G be a group written multiplicatively. We say that G has the small sumsets property if f...
Suppose that Y1, Y2, Y3 are finite sets and P ⊆ Y1 × Y2 × Y3. We say that P embeds in a group G if ...
AbstractIf X is an n-element set, we call a family G⊂PX a k-generator for X if every x⊂X can be expr...
For every infinite group G and every set of generators S of G, we construct a system of generators i...
The combinatorial notion of a "small set" in an abstract group was introduced by Bella and Malykhin....
A set S in a group G is said to be small if there exist infinitely many pairwise disjoint translat...
<p>A subset $X$ of a group $G$ is called $P$-small (almost $P$-small) if there exists an injective ...
Abstract. Answering a question of D.Dikranjan and I.Protasov we prove that each infinite Abelian gro...
[EN] We study the behaviour of large, small and medium subsets with respect to homomorphisms and pro...
AbstractA subset S of a finite group G invariably generates G if G=〈sg(s)|s∈S〉 for each choice of g(...
A subset U of a group G is called k-universal if U contains a translate of every k-element subset of...
AbstractYap (1983) shows that each set having small generators is in the class NP/poly which was int...
International audienceA group is small if it has countably many complete n-types over the empty set ...
For every prime p, we exhibit a finite p-group which cannot be generated by a set of elements, all h...
Let G be a group written multiplicatively.We say that G has the small sumsets property if for all po...
AbstractLet G be a group written multiplicatively. We say that G has the small sumsets property if f...
Suppose that Y1, Y2, Y3 are finite sets and P ⊆ Y1 × Y2 × Y3. We say that P embeds in a group G if ...
AbstractIf X is an n-element set, we call a family G⊂PX a k-generator for X if every x⊂X can be expr...
For every infinite group G and every set of generators S of G, we construct a system of generators i...
The combinatorial notion of a "small set" in an abstract group was introduced by Bella and Malykhin....
A set S in a group G is said to be small if there exist infinitely many pairwise disjoint translat...
<p>A subset $X$ of a group $G$ is called $P$-small (almost $P$-small) if there exists an injective ...
Abstract. Answering a question of D.Dikranjan and I.Protasov we prove that each infinite Abelian gro...
[EN] We study the behaviour of large, small and medium subsets with respect to homomorphisms and pro...
AbstractA subset S of a finite group G invariably generates G if G=〈sg(s)|s∈S〉 for each choice of g(...
A subset U of a group G is called k-universal if U contains a translate of every k-element subset of...
AbstractYap (1983) shows that each set having small generators is in the class NP/poly which was int...
International audienceA group is small if it has countably many complete n-types over the empty set ...
For every prime p, we exhibit a finite p-group which cannot be generated by a set of elements, all h...
Let G be a group written multiplicatively.We say that G has the small sumsets property if for all po...
AbstractLet G be a group written multiplicatively. We say that G has the small sumsets property if f...
Suppose that Y1, Y2, Y3 are finite sets and P ⊆ Y1 × Y2 × Y3. We say that P embeds in a group G if ...
AbstractIf X is an n-element set, we call a family G⊂PX a k-generator for X if every x⊂X can be expr...
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