Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 2, pp. 493-502
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A. N. Krasilnikov; A. L. Shmel'kin. Applications of the Magnus embedding in the theory of varieties of groups and Lie algebras. Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 2, pp. 493-502. http://geodesic.mathdoc.fr/item/FPM_1999_5_2_a7/
@article{FPM_1999_5_2_a7,
author = {A. N. Krasilnikov and A. L. Shmel'kin},
title = {Applications of {the~Magnus} embedding in the~theory of varieties of groups and {Lie} algebras},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {493--502},
year = {1999},
volume = {5},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_1999_5_2_a7/}
}
TY - JOUR
AU - A. N. Krasilnikov
AU - A. L. Shmel'kin
TI - Applications of the Magnus embedding in the theory of varieties of groups and Lie algebras
JO - Fundamentalʹnaâ i prikladnaâ matematika
PY - 1999
SP - 493
EP - 502
VL - 5
IS - 2
UR - http://geodesic.mathdoc.fr/item/FPM_1999_5_2_a7/
LA - ru
ID - FPM_1999_5_2_a7
ER -
%0 Journal Article
%A A. N. Krasilnikov
%A A. L. Shmel'kin
%T Applications of the Magnus embedding in the theory of varieties of groups and Lie algebras
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 1999
%P 493-502
%V 5
%N 2
%U http://geodesic.mathdoc.fr/item/FPM_1999_5_2_a7/
%G ru
%F FPM_1999_5_2_a7
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 $A\operatorname{wr}F/R$, 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.
