Injectors of Locally Soluble FC-Groups.
Isoperimetric inequalities and the homology of groups.
Just-non-SRI*-groups
Lie perfect, Lie central extension and generalization of nilpotency in multiplicative Lie algebras
This paper aims to introduce and explore the concept of Lie perfect multiplicative Lie algebras, with a particular focus on their connections to the central extension theory of multiplicative Lie algebras. The primary objective is to establish and provide proof for a range of results derived from Lie perfect multiplicative Lie algebras. Furthermore, the study extends the notion of Lie nilpotency by introducing and examining the concept of local nilpotency within multiplicative Lie algebras. The...
Linear groups with the maximal condition on subgroups of infinite central dimension.
Linear properties of poly-Fuchsian groups.
Locally finite groups with all subgroups either subnormal or nilpotent-by-Chernikov
Let G be a locally finite group satisfying the condition given in the title and suppose that G is not nilpotent-by-Chernikov. It is shown that G has a section S that is not nilpotent-by-Chernikov, where S is either a p-group or a semi-direct product of the additive group A of a locally finite field F by a subgroup K of the multiplicative group of F, where K acts by multiplication on A and generates F as a ring. Non-(nilpotent-by-Chernikov) extensions of this latter kind exist and are described in...
Locally nilpotent linear groups with the weak chain conditions on subgroups of infinite central dimension .
Locally soluble cofinitary groups with few fixed points.
Locally soluble groups with all nontrivial normal subgroups isomorphic.
Let G be an infinite, locally soluble group which is isomorphic to all its nontrivial normal subgroups. If G/G' has finite p-rank for p = 0 and for all primes p, then G is cyclic.
Locally soluble-by-finite groups with small deviation for non-subnormal subgroups
A group has subnormal deviation at most if, for every descending chain of non-subnormal subgroups of , for all but finitely many there is no infinite descending chain of non-subnormal subgroups of that contain and are contained in . This property , say, was investigated in a previous paper by the authors, where soluble groups with and locally nilpotent groups with were effectively classified. The present article affirms a conjecture from that article by showing that locally soluble-by-finite...
Medial and Distributively Generated Near-Rings.
On embedding properties of -groups.
On groups of plolynomial subgroup growth.
On Groups whose Contranormal Subgroups are Normally Complemented
2000 Mathematics Subject Classification: 20F16, 20E15.Groups in which every contranormal subgroup is normally complemented has been considered. The description of such groups G with the condition Max-n and such groups having an abelian nilpotent residual satisfying Min-G have been obtained.
On hypercentral groups
Let G be a hypercentral group. Our main result here is that if G/G’ is divisible by finite then G itself is divisible by finite. This extends a recent result of Heng, Duan and Chen [2], who prove in a slightly weaker form the special case where G is also a p-group. If G is torsion-free, then G is actually divisible.
On hypercentral subgroups of infinite groups
On locally finite minimal non-solvable groups
In the present work we consider infinite locally finite minimal non-solvable groups, and give certain characterizations. We also define generalizations of the centralizer to establish a result relevant to infinite locally finite minimal non-solvable groups.
On maximal subgroups of minimax groups
It is proved that a soluble residually finite minimax group is finite-by-nilpotent if and only if it has only finitely many maximal subgroups which are not normal.
On minimal non-PC-groups
A group is said to be a PC-group, if is a polycyclic-by-finite group for all . A minimal non-PC-group is a group which is not a PC-group but all of whose proper subgroups are PC-groups. Our main result is that a minimal non-PC-group having a non-trivial finite factor group is a finite cyclic extension of a divisible abelian group of finite rank.