Embedding the Outer Automorphism Group $\operatorname{Out}(F_n)$ of a Free Group of Rank $n$ in the Group $\operatorname{Out}(F_m)$ for $m>n$
Algebra i logika, Tome 41 (2002) no. 2, pp. 123-129
Voir la notice de l'article provenant de la source Math-Net.Ru
It is proved that for every $n\geqslant1$, the group $\operatorname{Out}(F_n)$ is embedded in the group $\operatorname{Out}(F_m)$ with $m=1+(n-1)k^n$, where $k$ is an arbitrary natural number coprime to $n-1$.
Keywords:
group of outer automorphisms, free group.
@article{AL_2002_41_2_a0,
author = {O. V. Bogopolskii and D. V. Puga},
title = {Embedding the {Outer} {Automorphism} {Group~}$\operatorname{Out}(F_n)$ of {a~Free} {Group} of {Rank~}$n$ in the {Group} $\operatorname{Out}(F_m)$ for $m>n$},
journal = {Algebra i logika},
pages = {123--129},
publisher = {mathdoc},
volume = {41},
number = {2},
year = {2002},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/AL_2002_41_2_a0/}
}
TY - JOUR
AU - O. V. Bogopolskii
AU - D. V. Puga
TI - Embedding the Outer Automorphism Group $\operatorname{Out}(F_n)$ of a Free Group of Rank $n$ in the Group $\operatorname{Out}(F_m)$ for $m>n$
JO - Algebra i logika
PY - 2002
SP - 123
EP - 129
VL - 41
IS - 2
PB - mathdoc
UR - http://geodesic.mathdoc.fr/item/AL_2002_41_2_a0/
LA - ru
ID - AL_2002_41_2_a0
ER -
%0 Journal Article
%A O. V. Bogopolskii
%A D. V. Puga
%T Embedding the Outer Automorphism Group $\operatorname{Out}(F_n)$ of a Free Group of Rank $n$ in the Group $\operatorname{Out}(F_m)$ for $m>n$
%J Algebra i logika
%D 2002
%P 123-129
%V 41
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2002_41_2_a0/
%G ru
%F AL_2002_41_2_a0
O. V. Bogopolskii; D. V. Puga. Embedding the Outer Automorphism Group $\operatorname{Out}(F_n)$ of a Free Group of Rank $n$ in the Group $\operatorname{Out}(F_m)$ for $m>n$. Algebra i logika, Tome 41 (2002) no. 2, pp. 123-129. http://geodesic.mathdoc.fr/item/AL_2002_41_2_a0/