# Presentations of finite simple groups: a computational approach

Robert Guralnick; William M. Kantor; Martin Kassabov; Alexander Lubotzky

Journal of the European Mathematical Society (2011)

- Volume: 013, Issue: 2, page 391-458
- ISSN: 1435-9855

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topGuralnick, 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 -

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