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A third-Engel 5-group

Published online by Cambridge University Press:  09 April 2009

I. D. Macdonald  and
B. H. Neumann
I. D. Macdonald
Affiliation:
The University of NewcastleNew South Wales
B. H. Neumann
Affiliation:
Australian National UniversityCanberra, A.C.T.
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In this paper a certain group with the third-Engel condition, that is a member of the variety defined by1 will be presented. Reasons for which its properties may be of interest are advanced in the present section.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 7 , Issue 4 , November 1967 , pp. 555 - 569
Copyright
Copyright © Australian Mathematical Society 1967

References

[1]Baer, Reinhold, “Nilpotent groups and their generalizations”, Trans. Amer. Math. Soc. 47 (1940), 393–434.CrossRefGoogle Scholar
[2]Gupta, Chander Kanta, “A bound for the class of certain nilpotent groups”, J. Austral. Math. Soc. 5 (1965), 506–511.Google Scholar
[3]Heineken, Hermann, “Engelsche Elemente der Länge drei”, Illinois J. Math. 5 (1961), 681–707.CrossRefGoogle Scholar
[4]Heineken, Hermann, “Über ein Levisches Nilpotenzkriterium”, Arch. Math. 12 (1961), 176–178.Google Scholar
[5]Higman, Graham, “Some remarks on varieties of groups”, Quart. J. Math. (Oxford Second Series) 10 (1959), 165–178.Google Scholar
[6]Kappe, Wolfgang, “Die A-Norm einer Gruppe”, Illinois J. Math. 5 (1961), 187–197.CrossRefGoogle Scholar
[7]Lazard, Michel, “Sur les groupes nilpotents et les anneaux de Lie”, Ann. Sci. Ecole Norm. Sup. (3) 71 (1954), 101–190.Google Scholar
[8]Levi, F. W., “Groups in which the commutator relation satisfies certain algebraic conditions”, J. Indian Math. Soc. 6 (1942), 87–97.Google Scholar
[9]Macdonald, I. D., “Generalisations of a classical theorem about nilpotent groups”, Illinois J. Math. 8 (1964), 556–570.Google Scholar
[10]Macdonald, I. D., “A theorem about critical ρ-groups”, Proc. Internal. Conf. Theory of Groups, Austral. Nat. Univ. Canberra, August 1965, 241–249 (Gordon and Breach, New York, 1966).Google Scholar
[11]Neumann, Hanna, Varieties of groups (Springer-Verlag, Berlin-Heidelberg-New York 1967).Google Scholar