Add to ORKGAbstract. In this paper we show that some finiteness properties on a centralizer of a particular subgroup can be inherited by the whole group. Among other things, we prove the following char-acterization of polycyclic groups: a soluble group G is polycyclic if and only if it contains a finitely generated subgroup H, formed by bounded left Engel elements, whose centralizer CG(H) is poly-cyclic. In the context of Černikov groups we obtain a more general result: a radical group is a Černikov group if and only if it contains a finitely generated subgroup, formed by left Engel elements, whose centralizer is a Černikov group. The aforementioned results gener-alize a theorem by Onishchuk and Zăıtsev about the centralizer of a finitely generate...
Let G be a finite group. A coprime commutator in G is any element that can be written as a commutato...
We study groups having the property that every non-cyclic subgroup contains its centralizer. The str...
We discuss various results on the number of commuting pairs and the sizes of the centralizers of a g...
Abstract. Let G be a group and let cent(G) denote the set of centralizers of single elements of G. A...
We study groups in which all infinite subgroups are centralizers. Such groups are periodic; we compl...
We consider the following two finiteness conditions on normalizers and centralizers in a group G: (i...
We consider formal maps in any finite dimension $d$ with coefficients in an integral domain $K$ with...
We study finite and profinite groups admitting an action by an elementary abelian group under which...
Let $q$ be a prime, $n$ a positive integer and $A$ an elementary abelian group of order $q^r$ with $...
Abstract. Let n and k be positive integers. We say that a group G satisfies the condition E(n) (resp...
We consider a finiteness condition on centralizers in a group G, namely that |C_G(x):⟨x⟩|<∞ for e...
Let be a group class (such as the class of all finite groups). Starting from , we can define the cla...
- The terminology is standard and follows D.J.Robinson, ”Finiteness conditions and generalized solub...
If R is a commutative ring, G is a nite group, and H is a subgroup of G, then the centralizer algeb...
Let G be a finite group. A coprime commutator in G is any element that can be written as a commutato...
We study groups having the property that every non-cyclic subgroup contains its centralizer. The str...
We discuss various results on the number of commuting pairs and the sizes of the centralizers of a g...
Abstract. Let G be a group and let cent(G) denote the set of centralizers of single elements of G. A...
We study groups in which all infinite subgroups are centralizers. Such groups are periodic; we compl...
We consider the following two finiteness conditions on normalizers and centralizers in a group G: (i...
We consider formal maps in any finite dimension $d$ with coefficients in an integral domain $K$ with...
We study finite and profinite groups admitting an action by an elementary abelian group under which...
Let $q$ be a prime, $n$ a positive integer and $A$ an elementary abelian group of order $q^r$ with $...
Abstract. Let n and k be positive integers. We say that a group G satisfies the condition E(n) (resp...
We consider a finiteness condition on centralizers in a group G, namely that |C_G(x):⟨x⟩|<∞ for e...
Let be a group class (such as the class of all finite groups). Starting from , we can define the cla...
- The terminology is standard and follows D.J.Robinson, ”Finiteness conditions and generalized solub...
If R is a commutative ring, G is a nite group, and H is a subgroup of G, then the centralizer algeb...
Let G be a finite group. A coprime commutator in G is any element that can be written as a commutato...
We study groups having the property that every non-cyclic subgroup contains its centralizer. The str...
We discuss various results on the number of commuting pairs and the sizes of the centralizers of a g...