Presentations of finite simple groups: a computational approach

Guralnick, Robert, et al. "Presentations of finite simple groups: a computational approach." Journal of the European Mathematical Society 013.2 (2011): 391-458. <http://eudml.org/doc/277739>.

@article{Guralnick2011,
abstract = {All finite simple groups of Lie type of rank $n$ over a field of size $q$, with the possible exception of the Ree groups $^2G_2(q)$, have presentations with at most 49 relations and bit-length $O(\texttt \{log\}\left.n +\texttt \{log\}\left.q)\right.\right.$. Moreover, $A_n$ and $S_n$ have presentations with 3 generators; 7 relations and bit-length $O(\texttt \{log\}\left.n)\right.$, while $\texttt \{SL\}(n,q)$ has a presentation with 6 generators, 25 relations and bit-length $O(\texttt \{log\}\left.n +\texttt \{log\}\left.q)\right.\right.$.},
author = {Guralnick, Robert, Kantor, William M., Kassabov, Martin, Lubotzky, Alexander},
journal = {Journal of the European Mathematical Society},
keywords = {presentations of finite groups; cohomology; profinite groups; efficient presentations; proficient presentation; finite simple groups; finite simple groups of Lie type; short presentations; generators and relations; bit-lengths; alternating groups; finite simple groups of Lie type; short presentations; generators and relations; bit-lengths; alternating groups},
language = {eng},
number = {2},
pages = {391-458},
publisher = {European Mathematical Society Publishing House},
title = {Presentations of finite simple groups: a computational approach},
url = {http://eudml.org/doc/277739},
volume = {013},
year = {2011},
}

TY - JOUR
AU - Guralnick, Robert
AU - Kantor, William M.
AU - Kassabov, Martin
AU - Lubotzky, Alexander
TI - Presentations of finite simple groups: a computational approach
JO - Journal of the European Mathematical Society
PY - 2011
PB - European Mathematical Society Publishing House
VL - 013
IS - 2
SP - 391
EP - 458
AB - All finite simple groups of Lie type of rank $n$ over a field of size $q$, with the possible exception of the Ree groups $^2G_2(q)$, have presentations with at most 49 relations and bit-length $O(\texttt {log}\left.n +\texttt {log}\left.q)\right.\right.$. Moreover, $A_n$ and $S_n$ have presentations with 3 generators; 7 relations and bit-length $O(\texttt {log}\left.n)\right.$, while $\texttt {SL}(n,q)$ has a presentation with 6 generators, 25 relations and bit-length $O(\texttt {log}\left.n +\texttt {log}\left.q)\right.\right.$.
LA - eng
KW - presentations of finite groups; cohomology; profinite groups; efficient presentations; proficient presentation; finite simple groups; finite simple groups of Lie type; short presentations; generators and relations; bit-lengths; alternating groups; finite simple groups of Lie type; short presentations; generators and relations; bit-lengths; alternating groups
UR - http://eudml.org/doc/277739
ER -