Geodesic
A weak Zassenhaus Lemma for discrete subgroups of Diff(I)
Akhmedov, Azer1
1Mathematics Department, North Dakota State University, Fargo, ND 58102, USA
Algebraic and Geometric Topology, Tome 14 (2014) no. 1, pp. 539-550
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We prove a weaker version of the Zassenhaus Lemma for subgroups of Diff(I). We also show that a group with commutator subgroup containing a non-Abelian free subsemigroup does not admit a C0–discrete faithful representation in Diff(I).

DOI : 10.2140/agt.2014.14.539
Classification : 37C05, 20F65
Keywords: diffeomorphism group of the interval, Zassenhaus Lemma, discrete subgroups of $\operatorname{Diff}(I)$

Akhmedov, Azer  1

1 Mathematics Department, North Dakota State University, Fargo, ND 58102, USA 
@article{10_2140_agt_2014_14_539,
     author = {Akhmedov, Azer},
     title = {A weak {Zassenhaus} {Lemma} for discrete subgroups of {Diff(I)}},
     journal = {Algebraic and Geometric Topology},
     pages = {539--550},
     year = {2014},
     volume = {14},
     number = {1},
     doi = {10.2140/agt.2014.14.539},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2014.14.539/}
}
TY  - JOUR
AU  - Akhmedov, Azer
TI  - A weak Zassenhaus Lemma for discrete subgroups of Diff(I)
JO  - Algebraic and Geometric Topology
PY  - 2014
SP  - 539
EP  - 550
VL  - 14
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2014.14.539/
DO  - 10.2140/agt.2014.14.539
ID  - 10_2140_agt_2014_14_539
ER  - 
%0 Journal Article
%A Akhmedov, Azer
%T A weak Zassenhaus Lemma for discrete subgroups of Diff(I)
%J Algebraic and Geometric Topology
%D 2014
%P 539-550
%V 14
%N 1
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2014.14.539/
%R 10.2140/agt.2014.14.539
%F 10_2140_agt_2014_14_539
Akhmedov, Azer. A weak Zassenhaus Lemma for discrete subgroups of Diff(I). Algebraic and Geometric Topology, Tome 14 (2014) no. 1, pp. 539-550. doi: 10.2140/agt.2014.14.539

[1] A Akhmedov, On free discrete subgroups of $\mathrm{Diff}(I)$, Algebr. Geom. Topol. 10 (2010) 2409

[2] B Farb, J Franks, Groups of homeomorphisms of one-manifolds, III: Nilpotent subgroups, Ergodic Theory Dynam. Systems 23 (2003) 1467

[3] A Navas, Growth of groups and diffeomorphisms of the interval, Geom. Funct. Anal. 18 (2008) 988

[4] A Navas, Sur les rapprochements par conjugasion en dimension $1$ et classe $C^1$, (2013)

[5] J F Plante, W P Thurston, Polynomial growth in holonomy groups of foliations, Comment. Math. Helv. 51 (1976) 567

[6] M S Raghunathan, Discrete subgroups of Lie groups, Ergeb. Math. Grenzgeb. 68, Springer (1972)

[7] G Szekeres, Regular iteration of real and complex functions, Acta Math. 100 (1958) 203

Cité par Sources :