Skip to main content Accessibility help
×
Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-30T19:56:44.593Z Has data issue: false hasContentIssue false

Lie methods in Engel groups

Published online by Cambridge University Press:  05 July 2011

Michael Vaughan-Lee
Affiliation:
Christ Church, Oxford
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

[1] S., Bachmuth and H.Y., Mochizuki, Third Engel groups and the Macdonald–Neumann conjecture, Bull. Austral. Math. Soc. 5 (1971), 379–386.Google Scholar
[2] N.D., Gupta and F., Levin, On soluble Engel groups and Lie algebras, Arch. Math. 34 (1980), 289–295.Google Scholar
[3] G., Havas, M.F., Newman, and M.R., Vaughan-Lee, A nilpotent quotient algorithm for graded Lie rings, J. Symbolic Comput. 9 (1990), 653–664.Google Scholar
[4] George, Havas and M.R., Vaughan-Lee, 4-Engel groups are locally nilpotent, Internat. J. Algebra Comput. 15 (2005), 649–682.Google Scholar
[5] H., Heineken, Engelsche Elemente der Länge drei, Illinois J. Math. 5 (1961), 681–707.Google Scholar
[6] G., Higman, On finite groups of exponent five, Proc. Camb. Phil. Soc. 52 (1956), 381–390.Google Scholar
[7] G., Higman, Some remarks on varieties of groups, Quart. J. Math. Oxford (2) 10 (1959), 165–178.Google Scholar
[8] L.C., Kappe and W.P., Kappe, On three Engel groups, Bull. Austral. Math. Soc. 7 (1972), 391–405.Google Scholar
[9] F.W., Levi, Groups in which the commutator operation satisfies certain algebraic conditions, J. Indian Math. Soc. 6 (1942), 87–97.Google Scholar
[10] M.F., Newman and Michael, Vaughan-Lee, Engel-4 groups of exponent 5 II. Orders, Proc. London Math. Soc. (3) 79 (1999), 283–317.Google Scholar
[11] W., Nickel, Computation of nilpotent Engel groups, J. Austral. Math. Soc. Ser. A 67 (1999), 214–222.Google Scholar
[12] Ju. P., Razmyslov, On Engel Lie algebras, Algebra i Logika 10 (1971), 33–44.Google Scholar
[13] G., Traustason, On 4-Engel groups, J. Algebra 178 (1995), 414–429.Google Scholar
[14] Gunnar, Traustason, Locally nilpotent 4-Engel groups are Fitting groups, J. Algebra 270 (2003), 7–27.Google Scholar
[15] Michael, Vaughan-Lee, On 4-Engel groups, L.M.S. J. Comput. Math. 10 (2007), 341–353.Google Scholar
[16] M.R., Vaughan-Lee, Engel-4 groups of exponent 5, Proc. London Math. Soc. 74 (1997), 306–334.Google Scholar
[17] M.R., Vaughan-Lee, An insoluble (p - 2)-Engel group of exponent, p, J. Algebra to appear.
[18] G.E., Wall, Multilinear Lie relators for varieties of groups, J. Algebra 157 (1993), 341–393.Google Scholar
[19] J.S., Wilson, Two-generator conditions for residually finite groups, Bull. London Math. Soc. 23 (1991), 239–248.Google Scholar
[20] E.I., Zel'manov, Engel Lie algebras, Dokl. Akad. Nauk SSSR 292 (1987), 265–268.Google Scholar
[21] E.I., Zel'manov, The solution of the restricted Burnside problem for groups of odd exponent, Izv. Math. USSR 36 (1991), 41–60.Google Scholar
[22] E.I., Zel'manov, The solution of the restricted Burnside problem for 2-groups, Mat. Sb. 182 (1991), 568–592.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
×