Geodesic
Random generation of finite and profinite groups and group enumeration
Andrei Jaikin-Zapirain1 ; László Pyber 2
1 Departamento de Matemáticas<br/>Universidad Autónoma de Madrid<br/>Spain<br/><br/>and<br/><br/>Instituto de Ciencias Matemáticas<br/>CSIC-UAM-UC3M-UCM
2 Alfréd Rényi Institute of Mathematics<br/>Hungarian Academy of Sciences<br/>Budapest<br/> Hungary
Annals of mathematics, Tome 173 (2011) no. 2, pp. 769-814.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We obtain a surprisingly explicit formula for the number of random elements needed to generate a finite $d$-generator group with high probability. As a corollary we prove that if $G$ is a $d$-generated linear group of dimension $n$ then $cd+\log n$ random generators suffice.
DOI : 10.4007/annals.2011.173.2.4

Andrei Jaikin-Zapirain 1 ; László Pyber  2

1 Departamento de Matemáticas<br/>Universidad Autónoma de Madrid<br/>Spain<br/><br/>and<br/><br/>Instituto de Ciencias Matemáticas<br/>CSIC-UAM-UC3M-UCM
2 Alfréd Rényi Institute of Mathematics<br/>Hungarian Academy of Sciences<br/>Budapest<br/> Hungary 
@article{10_4007_annals_2011_173_2_4,
     author = {Andrei Jaikin-Zapirain and L\'aszl\'o Pyber },
     title = {Random generation of finite and profinite groups and group enumeration},
     journal = {Annals of mathematics},
     pages = {769--814},
     publisher = {mathdoc},
     volume = {173},
     number = {2},
     year = {2011},
     doi = {10.4007/annals.2011.173.2.4},
     mrnumber = {2776362},
     zbl = {05960671},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.173.2.4/}
}
TY  - JOUR
AU  - Andrei Jaikin-Zapirain
AU  - László Pyber 
TI  - Random generation of finite and profinite groups and group enumeration
JO  - Annals of mathematics
PY  - 2011
SP  - 769
EP  - 814
VL  - 173
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.173.2.4/
DO  - 10.4007/annals.2011.173.2.4
LA  - en
ID  - 10_4007_annals_2011_173_2_4
ER  - 
%0 Journal Article
%A Andrei Jaikin-Zapirain
%A László Pyber 
%T Random generation of finite and profinite groups and group enumeration
%J Annals of mathematics
%D 2011
%P 769-814
%V 173
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.173.2.4/
%R 10.4007/annals.2011.173.2.4
%G en
%F 10_4007_annals_2011_173_2_4
Andrei Jaikin-Zapirain; László Pyber . Random generation of finite and profinite groups and group enumeration. Annals of mathematics, Tome 173 (2011) no. 2, pp. 769-814. doi : 10.4007/annals.2011.173.2.4. http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.173.2.4/

Cité par Sources :