FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1999, VOLUME 5, NUMBER 2, PAGES 493-502

Applications of the Magnus embedding in the theory of varieties of groups and Lie algebras

A. N. Krasilnikov
A. L. Shmelkin

Abstract

View as HTML     View as gif image    View as LaTeX source

We give a survey of results of the theory of varieties of groups and Lie algebras which were proved using the Magnus embedding or its generalizations (the Magnus embedding is the embedding of a group of the form $F/R\text{'}$ into the wreath product $\$\; A\; wr\; F/R\; \$$, where $A$ is a free Abelian group). We exhibit short proofs of the embedding theorem as well as of the criterion for an element of the wreath product to belong to the embedded group.

All articles are published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/99/992/99208h.htm
Last modified: July 6, 1999