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The local nilpotence theorem for 4-Engel groups revisited | ||
| International Journal of Group Theory | ||
| مقاله 5، دوره 4، شماره 3، آذر 2015، صفحه 21-75 اصل مقاله (347.14 K) | ||
| نوع مقاله: Ischia Group Theory 2014 | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2015.5551 | ||
| نویسنده | ||
| Gunnar Traustason* | ||
| University of Bath | ||
| چکیده | ||
| The proof of the local nilpotence theorem for $4$-Engel groups was completed by G. Havas and M. Vaughan-Lee in 2005. The complete proof on the other hand is spread over several articles and the aim of this paper is to give a complete coherent linear version. In the process we are also able to make a few simplifications and in particular we are able to merge two of the key steps into one. | ||
| کلیدواژه‌ها | ||
| 4-Engel؛ nilpotence؛ left Engel | ||
| مراجع | ||
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K. W. Gruenberg (1953) Two theorems on Engel groups Proc. Cambridge Philos. Soc. 49, 377-380
G. Havas and M. R. Vaughan-Lee (2005) 4-Engel groups are locally nilpotent Internat. J. Algebra Comput. 15, 649-682
H. Heineken (1961) Engelsche Elemente der Lange drei Illinois J. Math. 5, 681-707
Y. K. Kim and A. H. Rhemtulla (1995) Weak maximality condition and polycyclic groups Proc. Amer. Math. Soc. 123, 711-714
P. Longobardi and M. Maj (1999) Semigroup identities and Engel groups Groups St. Andrews 1997 in Bath II, London Math. So c., Lecture Note Series, Cambridge Univ. Pess, Cambridge 261, 527-531
M. Newell (1996) On right-Engel elements of length three Proc. Roy. Irish Acad. Sect. A 96, 17-24
W. Nickel (1999) Computation of nilp otent Engel groups J. Austral. Math. Soc. Ser. A 67, 214-222
G. Traustason (1995) On 4-Engel groups J. Algebra 178, 414-429
G. Traustason (1999) Semigroup identities in 4-Engel groups J. Group Theory 2, 39-46
G. Traustason (2005) Two generator 4-Engel groups Internat. J. Algebra Comput. 15, 309-316
G. Traustason (2005) A note on the local nilpotence of 4-Engel groups Internat. J. Algebra Comput. 15, 757-764
G. Traustason (2011) Engel groups Groups St Andrews 2009 in Bath, Volume I I, London Math. So c. Lecture Note serie, Cambridge University Press, Cambridge 388, 520-550
M. R. Vaughan-Lee (1997) Engel-4 groups of exponent 5 Proc. London Math. Soc. (3) 74, 306-334
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