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A third-Engel 5-group

Published online by Cambridge University Press:  09 April 2009

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
Copyright
Copyright © Australian Mathematical Society 1967

References

[1]Baer, Reinhold, “Nilpotent groups and their generalizations”, Trans. Amer. Math. Soc. 47 (1940), 393434.CrossRefGoogle Scholar
[2]Gupta, Chander Kanta, “A bound for the class of certain nilpotent groups”, J. Austral. Math. Soc. 5 (1965), 506511.Google Scholar
[3]Heineken, Hermann, “Engelsche Elemente der Länge drei”, Illinois J. Math. 5 (1961), 681707.CrossRefGoogle Scholar
[4]Heineken, Hermann, “Über ein Levisches Nilpotenzkriterium”, Arch. Math. 12 (1961), 176178.Google Scholar
[5]Higman, Graham, “Some remarks on varieties of groups”, Quart. J. Math. (Oxford Second Series) 10 (1959), 165178.Google Scholar
[6]Kappe, Wolfgang, “Die A-Norm einer Gruppe”, Illinois J. Math. 5 (1961), 187197.CrossRefGoogle Scholar
[7]Lazard, Michel, “Sur les groupes nilpotents et les anneaux de Lie”, Ann. Sci. Ecole Norm. Sup. (3) 71 (1954), 101190.Google Scholar
[8]Levi, F. W., “Groups in which the commutator relation satisfies certain algebraic conditions”, J. Indian Math. Soc. 6 (1942), 8797.Google Scholar
[9]Macdonald, I. D., “Generalisations of a classical theorem about nilpotent groups”, Illinois J. Math. 8 (1964), 556570.Google Scholar
[10]Macdonald, I. D., “A theorem about critical ρ-groups”, Proc. Internal. Conf. Theory of Groups, Austral. Nat. Univ. Canberra, August 1965, 241249 (Gordon and Breach, New York, 1966).Google Scholar
[11]Neumann, Hanna, Varieties of groups (Springer-Verlag, Berlin-Heidelberg-New York 1967).Google Scholar