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

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```
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 $F/R'$ into the wreath product
$A \mathrel{wr} F/R$,
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.
```

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Location: http://mech.math.msu.su/~fpm/eng/99/992/99208t.htm

Last modified: July 6, 1999