a result of dixon‎, ‎evans and smith shows that if $g$ is a locally (soluble-by-finite) group whose proper subgroups are (finite rank)-by-abelian‎, ‎then $g$ itself has this property‎, ‎i.e‎. ‎the commutator subgroup of $g$ has finite rank‎. ‎it is proved here that if $g$ is a locally (soluble-by-finite) group whose proper subgroups have minimax commutator subgroup‎, ‎then also the commutator s...

Analysis of the electromagnetic processes is organized beside this article in electric circuit with semiconductor commutator. Mathematical model created for analysis electro-magnetic converter width pulsed regulation output voltage. The broughted graphs, which reflect circuit. Method much parametric functions was used when performing calculation. mathematical fifteen zoned regulations Article d...

Mass formulae for light meson multiplets derived by means of exotic commutator technique can be written for complex masses. Then the real parts of the formulae give the well known mass formulae (GM-O, Schwinger and Ideal) and the imaginary ones give appropriate sum rules for total hadronic widths. Most of the observed meson nonets satisfy Schwinger mass formula (Schwinger nonet). The width sum ...

Various sum rules for multiple giant dipole resonance states are derived. For the triple giant dipole resonance states, the energy-weighted sum of the transition strengths requires a model to be related to those of the single and double giant dipole resonance states. It is also shown that the non-diagonal matrix elements of the double commutator between the dipole operator and the nuclear Hamil...

We introduce a new notion of commutator which depends on a choice of subvariety in any variety of Ω-groups. We prove that this notion encompasses Higgins’s commutator, Fröhlich’s central extensions and the Peiffer commutator of precrossed modules.

We investigate commutator operations on compatible uniformities. We present a commutator operation for uniformities in the congruence-modular case which extends the commutator on congruences, and explore its properties. Introduction The purpose of this paper is to generalize the commutator of congruences to a commutator of compatible uniformities. Commutator theory (on congruences) works best f...

We develop the theories of the strong commutator, the rectangular commutator, the strong rectangular commutator, as well as a solvability theory for the nonmodular TC commutator. These theories are used to show that each of the following sets of statements are equivalent for a variety V of algebras. (I) (a) V satisfies a nontrivial congruence identity. (b) V satisfies an idempotent Maltsev cond...

In this paper, we verify the solvability of free product of finite cyclic groups with topological methods. We use Cayley graphs and Everitt methods to construct suitable 2-complexes corresponding to the presentations of groups and their commutator subgroups. In particular, using these methods, we prove that the commutator subgroup of $mathbb{Z}_{m}*mathbb{Z}_{n}$ is free of rank $(m-1)(n-1)$ fo...