Results 221 to 230 of about 137,024 (263)
Some of the next articles are maybe not open access.
On Locally Graded Minimal Non-(finite-by-hypercentral) Groups
Bulletin of the Malaysian Mathematical Sciences Society, 2020Let \(\mathfrak{X}\) be a class of groups. A group is said to be minimal non-\(\mathfrak{X}\) if it does not belong to \(\mathfrak{X}\) while every of its proper subgroup is a \(\mathfrak{X}\)-group. In the paper under review, the authors study the class of locally graded minimal non-(finite-by-hypercentral) groups. The main result of this paper states
Azra, Souad, Trabelsi, Nadir
openaire +2 more sources
Locally graded minimal non CC-groups arep-groups
Archiv der Mathematik, 1991The group \(G\) is a \(CC\)-group if \(G/C_ G(x^ G)\) is Chernikov for all \(x\in G\). If \(G\) is not a \(CC\)-group but all its proper subgroups are \(CC\)-groups \(G\) is said to be a minimal non \(CC\)-group. \textit{J. Otal} and \textit{J. M. Peña} [Commun. Algebra 16, 1231-1242 (1988; Zbl 0644.20025)] have shown that a locally graded minimal non-\
Hartley, B. +2 more
openaire +2 more sources
On Minimal Non-(residually Nilpotent) Locally Graded Groups
Mediterranean Journal of Mathematics, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +2 more sources
Algebra Colloquium, 2016
Let n ≠ 0, 1 be an integer and [Formula: see text] be the variety of n-Bell groups defined by the law [xn,y][x,yn]-1= 1. Let [Formula: see text] be the class of groups in which for any infinite subsets X and Y there exist x ∈ X and y ∈ Y such that [xn,y][x,yn]-1= 1. In this paper we prove [Formula: see text], where [Formula: see text] and [Formula: see
openaire +2 more sources
Let n ≠ 0, 1 be an integer and [Formula: see text] be the variety of n-Bell groups defined by the law [xn,y][x,yn]-1= 1. Let [Formula: see text] be the class of groups in which for any infinite subsets X and Y there exist x ∈ X and y ∈ Y such that [xn,y][x,yn]-1= 1. In this paper we prove [Formula: see text], where [Formula: see text] and [Formula: see
openaire +2 more sources
On the Structure of Locally Graded $$\overline T $$ -Groups
Mathematical Notes, 2002A group \(G\) is said to be a `T-group' if all its subnormal subgroups are normal, i.e. if normality in \(G\) is a transitive relation; moreover, \(G\) is called a `\(\overline{\text{T}}\)-group' if every subgroup of \(G\) is a T-group. In the 14-th edition of the Kourovka Notebook (1999; Zbl 0943.20003 and Zbl 0943.20004), the reviewer asked whether ...
Larin, S. V., Sozutov, A. I.
openaire +2 more sources
Structure of locally graded nonnilpotent CDN[]-groups
Ukrainian Mathematical Journal, 1997The main result of the paper is a list of non-nilpotent locally graded groups with additional conditions on subgroups. All groups of the list are finite dispersive groups.
openaire +3 more sources
Locally graded groups with a Bell condition on infinite subsets
Journal of Group Theory, 2009For any class of groups \(\mathcal X\), let \(\mathcal X^*\) denote the class of all groups \(G\) such that every infinite subset of \(G\) contains a pair of distinct elements which generate an \(\mathcal X\)-subgroup of \(G\). Is it true that a group in \(\mathcal X^*\) contributes to \(\mathcal X\)? This is a famous problem of P. Erdős. \textit{B. H.
DELIZIA, Costantino, TORTORA, ANTONIO
openaire +2 more sources
On locally graded $n$-Engel and positively $n$-Engel groups
Publicationes Mathematicae Debrecen, 2009Summary: We discuss four problems concerning \(n\)-Engel and so called positively \(n\)-Engel groups. As the answer to one of them we prove that in the class of locally graded groups every positively \(n\)-Engel group is locally nilpotent, which extends a similar result of \textit{D. M. Riley} [J. Group Theory 4, No.
Bajorska, Beata, Macedońska, Olga
openaire +2 more sources
Factorization theorems for locally graded groups
Ukrainian Mathematical Journal, 1983Proof. Note that the normalizer N =NG(H) is factorable with respect to the decomposition G =AB (see [2], Lemma 1.2 and the following remark). Suppose H is infinite and locally graded. By Lemma 7 of [I], it contains a chain of N-invariant subgroups H =HoDHi~...~Hi~ ..., i =0, i, 2, ..., such that each index [Hi:Hi+1 [ is finite and different from unity.
openaire +2 more sources
Quotient groups of locally graded groups and groups of certain Kurosh-Chernikov classes
Ukrainian Mathematical Journal, 1998The paper deals with the class of locally graded groups such that each non-unit finitely generated subgroup of the group contains a non-unit subgroup of finite index; the class of RN-groups consists of groups with solvable subinvariant subgroup system; the class of RI-groups consists of groups with solvable invariant system.
Chernikov, N. S., Trebenko, D. Ya.
openaire +2 more sources