Imperial College London
Professor Martin Liebeck

ProfessorMartinLiebeck

Faculty of Natural Sciences, Department of Mathematics

Head of Pure Mathematics Section/Prof of Pure Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8490m.liebeck Website

 
 
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Location

 

665Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Bridson:2019:10.1007/s00222-019-00892-3,
author = {Bridson, MR and Evans, DM and Liebeck, MW and Segal, D},
doi = {10.1007/s00222-019-00892-3},
journal = {Inventiones Mathematicae},
pages = {623--648},
title = {Algorithms determining finite simple images of finitely presented groups},
url = {http://dx.doi.org/10.1007/s00222-019-00892-3},
volume = {218},
year = {2019}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection? We prove both positive and negative results. For a collection of finite simple groups that contains infinitely many alternating groups, or contains classical groups of unbounded dimensions, we prove that there is no such algorithm. On the other hand, for families of simple groups of Lie type of bounded rank, we obtain positive results. For example, for any fixed untwisted Lie type X there is an algorithm that determines whether or not any given finitely presented group has simple images of the form X(q) for infinitely many q, and if there are finitely many, the algorithm determines them.
AU  - Bridson,MR
AU  - Evans,DM
AU  - Liebeck,MW
AU  - Segal,D
DO  - 10.1007/s00222-019-00892-3
EP  - 648
PY  - 2019///
SN  - 0020-9910
SP  - 623
TI  - Algorithms determining finite simple images of finitely presented groups
T2  - Inventiones Mathematicae
UR  - http://dx.doi.org/10.1007/s00222-019-00892-3
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000505172700006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - https://link.springer.com/article/10.1007%2Fs00222-019-00892-3
UR  - http://hdl.handle.net/10044/1/70524
VL  - 218
ER  -
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