Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-07-04T22:04:48.739Z Has data issue: false hasContentIssue false

Words and groups

Published online by Cambridge University Press:  05 July 2011

Dan Segal
Affiliation:
All Souls College, U.K.
C. M. Campbell
Affiliation:
University of St Andrews, Scotland
M. R. Quick
Affiliation:
University of St Andrews, Scotland
E. F. Robertson
Affiliation:
University of St Andrews, Scotland
C. M. Roney-Dougal
Affiliation:
University of St Andrews, Scotland
G. C. Smith
Affiliation:
University of Bath
G. Traustason
Affiliation:
University of Bath
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[A] M., Abért, On the probability of satisfying a word in a group, J. Group Theory 9 (2006), 685–694.Google Scholar
[BNP] L., Babai, N., Nikolov and L., Pyber, Expansion and product decompositions of finite groups: variations on a theme of Gowers, to appear.
[B1] A., Borel, Linear algebraic groups, 2nd ed., Springer-Verlag, New York, 1991.Google Scholar
[B2] A., Borel, On free subgroups of semi-simple groups, L'Enseignement Math. 29 (1983), 151–164.Google Scholar
[C] P. J., Cameron, Permutation groups, London Math. Soc. Student Texts 45, Cambridge Univ. Press, Cambridge, 1999.Google Scholar
[CF] J. W. S., Cassels and A., Fröhlich, Algebraic Number Theory, Academic Press, London, 1967.Google Scholar
[Co] P. M., Cohn, Algebra 2nd ed., Vol. 3, John Wiley, Chichester, 1991.Google Scholar
[GL] R. M., Guralnick and F., Lübeck, On p-singular elements in Chevalley groups in characteristic p, in Groups and computation III, 169–182, Ohio State Univ. Math. Res. Inst. Publ. 8, de Gruyter, Berlin, 2001.Google Scholar
[H] J. E., Humpreys, Linear algebraic groups, Springer-Verlag, New York, 1975.Google Scholar
[I] I. M., Isaacs, Character theory of finite groups, Academic Press, New York, 1976.Google Scholar
[JZ] A., Jaikin-Zapirain, On the verbal width of finitely generated pro-p groups, Revista Mat. Iberoamericana 24 (2008), 617–630.Google Scholar
[J] G. A., Jones, Varieties and simple groups, J. Austral. Math. Soc. 17 (1974), 163–173.Google Scholar
[L] M., Larsen, Word maps have large image, Israel J. Math. 139 (2004), 149–156.Google Scholar
[LaSh] M., Larsen and A., Shalev, Word maps and Waring type problems, J. Amer. Math. Soc. 22 (2009), 437–466.Google Scholar
[LN] R., Lidl and H., Niederreiter, Finite Fields (2nd Edn), Encyclopedia of Mathematics and its Applications 20, Cambridge Univ. Press, Cambridge, 1996.Google Scholar
[LiSh] M., Liebeck and A., Shalev, Diameter of simple groups: sharp bounds and applications, Annals of Math. 154 (2001), 383–406.Google Scholar
[LiSh2] M., Liebeck and A., Shalev, Simple groups, permutation groups and probability, J. Amer. Math. Soc. 12 (1999), 497–520.Google Scholar
[LOST] M., Liebeck, E., O'Brien, A., Shalev and P., Tiep, The Ore conjecture, J. European Math. Soc. 12 (2010), 939–1008.Google Scholar
[LS] A., Lubotzky and D., Segal, Subgroup growth, Birkhäuser, Basel, 2003.Google Scholar
[M] Ju. I., Merzljakov, Algebraic linear groups as full groups of automorphisms and the closure of their verbal subgroups (Russian; English summary), Algebra i Logika Sem. 6 (1967) no. 1, 83–94.Google Scholar
[MZ] C., Martinez and E., Zelmanov, Products of powers in finite simple groups, Israel J. Math. 96 (1996), 469–479.Google Scholar
[N] N., Nikolov, A product decomposition for the classical quasisimple groups, J. Group Theory 10 (2007), 43–53.Google Scholar
[NP] N., Nikolov and L., Pyber, Product decompositions of quasi-random groups and a Jordan-type theorem, to appear. See arXiv:math/0703343.
[NS] N., Nikolov and D., Segal, A characterization of finite soluble groups, Bull. London Math. Soc. 39 (2007), 209–213.Google Scholar
[NS2] N., Nikolov and D., Segal, On finitely generated profinite groups, I: strong completeness and uniform bounds, Annals of Math. 165 (2007), 171–238.Google Scholar
[NS3] N., Nikolov and D., Segal, On finitely generated profinite groups, II: products in quasisimple groups, Annals of Math. 165 (2007), 239–273.Google Scholar
[NS4] N., Nikolov and D., Segal, Powers in finite groups, Groups, Geometry and Dynamics, to appear. See arXiv:0909.6439
[PR] V. P., Platonov and A. S., Rapinchuk, Algebraic groups and number theory, Algebraic groups and number theory, Academic Press, New York, 1994.Google Scholar
[P] F., Point, Ultraproducts and Chevalley groups, Arch. Math. Logic 38 (1999), 355–372.Google Scholar
[SW] J., Saxl and J. S., Wilson, A note on powers in simple groups, Math. Proc. Cambridge Philos. Soc. 122 (1997), 91–94.Google Scholar
[S] D., Segal, Words: notes on verbal width in groups, London Math. Soc. Lecture Notes Series 361, Cambridge Univ. Press, Cambridge, 2009.Google Scholar
[S1] D., Segal, Closed subgroups of profinite groups, Proc. London Math. Soc. 81 (2000), 29–54.Google Scholar
[Sh] A., Shalev, Word maps, conjugacy classes and a non-commutative Waring-type theorem, Annals of Math. 170 (2009), 1383–1416.Google Scholar
[Wa] E., Warning, Bemerkung zur vorstehenden Arbeit von Herr Chevalley, Abh. Math. Sem. Univ. Hamburg 11 (1936), 76–83.Google Scholar
[W] B. A. F., Wehrfritz, Infinite linear groups, Springer-Verlag, Berlin, 1973.Google Scholar
[Wi] J. S., Wilson, On simple pseudofinite groups, J. London Math. Soc. 51 (1995), 471–490.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×