Skip to main content

Efficient presentations for finite simple groups and related groups

  • Conference paper
  • First Online:
Groups — Korea 1988

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1398))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. F.R. Beyl and J. Tappe, Group extensions, representations and the Schur multiplicator, Lecture Notes in Mathematics 958, Springer-Verlag, Berlin, 1982.

    MATH  Google Scholar 

  2. C.M. Campbell and E.F. Robertson, ‘A deficiency zero presentation for SL(2,p)', Bull. London Math. Soc. 12(1980), 17–20.

    Article  MathSciNet  MATH  Google Scholar 

  3. C.M. Campbell and E.F. Robertson, ‘The efficiency of simple groups of order<105', Comm. Algebra 10(1982), 217–225.

    Article  MathSciNet  MATH  Google Scholar 

  4. C.M. Campbell and E.F. Robertson, ‘Some problems in group presentations', J. Korean Math. Soc. 19(1983), 59–64.

    MathSciNet  MATH  Google Scholar 

  5. C.M. Campbell and E.F. Robertson, ‘On a class of groups related to SL(2,2n)', in Computational Group Theory (ed. M.D. Atkinson, Academic Press, London, 1984), 43–49.

    Google Scholar 

  6. C.M. Campbell and E.F. Robertson, ‘Presentations for the simple groups G, 105<‖G‖<106', Comm. Algebra 12(1984), 2643–2663.

    Article  MathSciNet  MATH  Google Scholar 

  7. C.M. Campbell and E.F. Robertson, ‘A CAYLEY file of finite simple groups G, 105<‖G‖<106', EUROCAL '85 (Lecture Notes in Computer Science 204, Springer-Verlag, Berlin, 1985), 243–244.

    Google Scholar 

  8. C.M. Campbell and E.F. Robertson, ‘Computing with finite simple groups and their covering groups', in Computers in Algebra (ed. M.C. Tangora, Marcel Dekker, New York, 1988), 17–26.

    Google Scholar 

  9. C.M. Campbell, T. Kawamata, I. Miyamoto, E.F. Robertson and P.D. Williams, ‘Deficiency zero presentations for certain perfect groups', Proc. Royal Soc. Edinburgh 103A (1986), 63–71.

    Article  MathSciNet  MATH  Google Scholar 

  10. C.M. Campbell, E.F. Robertson and P.D. Williams, ‘On presentations of PSL(2,p n)', submitted for publication.

    Google Scholar 

  11. J.J. Cannon, J. McKay and K-C. Young, ‘The non-abelian simple groups G, ‖G‖<105 — presentations', Comm. Algebra 7(1979) 1397–1406.

    Article  MathSciNet  MATH  Google Scholar 

  12. J.H. Conway, R.T. Curtis, S.P. Norton, R.A. Parker and R.A. Wilson, Atlas of Finite groups: Maximal Subgroups and Ordinary Characters for Simple Groups (Clarendon Press, Oxford, 1985).

    MATH  Google Scholar 

  13. A. Jamali, Computing with simple groups: maximal subgroups and presentations, Ph.D. thesis, University of St. Andrews, 1988.

    Google Scholar 

  14. A. Jamali and E.F. Robertson, ‘Efficient presentations for certain simple groups', Comm. Algebra, to appear.

    Google Scholar 

  15. G. Karpilovsky, The Schur multiplier (Oxford University Press, Oxford, 1987).

    MATH  Google Scholar 

  16. P.E. Kenne, ‘Presentations for some direct products of groups', Bull. Austral. Math. Soc. 28(1983), 131–133.

    Article  MathSciNet  MATH  Google Scholar 

  17. P.E. Kenne, ‘Efficient presentations for simple groups', The Cayley Bulletin 2(1985), 38.

    Google Scholar 

  18. P.E. Kenne, ‘Efficient presentations for three simple groups', Comm. Algebra 14(1986), 797–800.

    Article  MathSciNet  MATH  Google Scholar 

  19. M.A. Kervaire, ‘Multiplicateurs de Schur et K-theorie', in Essays on Topology and Related Topics, Memoires dédiés à Georges de Rham (eds. A. Haefliger and R. Narasimhan, Springer-Verlag, Berlin, 1970), 212–225.

    Chapter  Google Scholar 

  20. J. McKay and K-C. Young, ‘The non-abelian simple groups G, ‖G‖<106-minimal generating pairs', Math. Comp. 33(1979), 812–814.

    MathSciNet  MATH  Google Scholar 

  21. E.F. Robertson, Efficiency of finite simple groups and their covering groups', Contemp. Math. 45(1985), 287–294.

    Article  MathSciNet  Google Scholar 

  22. I. Schur, ‘Untersuchungen über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen', J. Reine Angew. Math. 132(1907), 85–137.

    MathSciNet  MATH  Google Scholar 

  23. J.G. Sunday, ‘Presentations of the groups SL(2,m) and PSL(2,m)', Canad. J. Math. 24(1972), 1129–1131.

    Article  MathSciNet  MATH  Google Scholar 

  24. R.G. Swan, ‘Minimal resolution for finite groups', Topology 4(1965), 193–208.

    Article  MathSciNet  MATH  Google Scholar 

  25. J.W. Wamsley, The deficiency of finite groups, Ph.D. thesis, University of Queensland, 1968.

    Google Scholar 

  26. J. Wiegold, ‘The Schur multiplier', in Groups — St Andrews 1981 (eds. C.M. Campbell and E.F. Robertson, L.M.S. Lecture Notes 71, Cambridge University Press, Cambridge, 1982), 137–154.

    Chapter  Google Scholar 

  27. P.D. Williams, Presentations of linear groups, Ph.D. thesis, University of St Andrews, 1982.

    Google Scholar 

  28. H.J. Zassenhaus, ‘A presentation of the groups PSL(2,p) with three defining relations', Canad. J. Math. 21(1969), 310–311.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Ann Chi Kim Bernhard H. Neumann

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag

About this paper

Cite this paper

Campbell, C.M., Robertson, E.F., Williams, P.D. (1989). Efficient presentations for finite simple groups and related groups. In: Kim, A.C., Neumann, B.H. (eds) Groups — Korea 1988. Lecture Notes in Mathematics, vol 1398. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086240

Download citation

  • DOI: https://doi.org/10.1007/BFb0086240

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51695-8

  • Online ISBN: 978-3-540-46756-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics