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Lie perfect, Lie central extension and generalization of nilpotency in multiplicative Lie algebras

Dev Karan Singh, Mani Shankar Pandey, Shiv Datt Kumar (2024)

Czechoslovak Mathematical Journal

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.

L.A. Kurdachenko, I.Ya. Subbotin (2006)

Publicacions Matemàtiques

Linear properties of poly-Fuchsian groups.

F.E.A. Johnson (1994)

Collectanea Mathematica

Locally finite groups with all subgroups either subnormal or nilpotent-by-Chernikov

Giovanni Cutolo, Howard Smith (2012)

Open Mathematics

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 .

L. A. Kurdachenko, J. M. Muñoz-Escolano, J. Otal (2008)

Publicacions Matemàtiques

Locally soluble cofinitary groups with few fixed points.

B.A.F. Wehrfritz (1997)

Forum mathematicum

Locally soluble groups with all nontrivial normal subgroups isomorphic.

John C. Lennox, Howard Smith, James Wiegold (1994)

Publicacions Matemàtiques

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

Leonid A. Kurdachenko, Howard Smith (2007)

Commentationes Mathematicae Universitatis Carolinae

A group $G$ has subnormal deviation at most $1$ if, for every descending chain $H_{0} > H_{1} > \dots$ of non-subnormal subgroups of $G$ , for all but finitely many $i$ there is no infinite descending chain of non-subnormal subgroups of $G$ that contain $H_{i + 1}$ and are contained in $H_{i}$ . This property $𝔓$ , say, was investigated in a previous paper by the authors, where soluble groups with $𝔓$ and locally nilpotent groups with $𝔓$ were effectively classified. The present article affirms a conjecture from that article by showing that locally soluble-by-finite...

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