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Engel-like elements in infinite soluble groups

Published online by Cambridge University Press:  20 January 2009

Rolf R. A. Brandl  and
Christopher J. B. Brookes
Rolf R. A. Brandl
Affiliation:
Mathematisches InstitutAm Hubland 12 D-8700 Würzburg, West Germany
Christopher J. B. Brookes
Affiliation:
Corpus Christi CollegeCambridge CB2 1RHEngland
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In [1] the first author considered the following Engel-like condition for a pair of elements x, y of a group G.

There exist r = r(x, y)≧0 and d = d(x, y)≧1 such that[x,ry] = [x,r+dy]. (*)

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 3 , October 1989 , pp. 337 - 343
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

REFERENCES

1.Brandl, R., Infinite soluble groups with Engel cycles: a finiteness condition, Math. Z. 182 (1983), 259–264.CrossRefGoogle Scholar
2.Brookes, C. J. B., Engel elements of soluble groups, Bull. London Math. Soc. 18 (1986), 7–10.CrossRefGoogle Scholar
3.Gruenberg, K. W., The Engel elements of a soluble group, Illinois J. Math. 3 (1959), 151–168.CrossRefGoogle Scholar
4.Heineken, H., Eine Bemerkung über engelsche Elemente, Arch. Math. 11 (1960), 321.CrossRefGoogle Scholar
5.Kropholler, P. H., On finitely generated soluble groups with no large wreath product sections, Proc. London Math. Soc. (3) 49 (1984), 155–169.CrossRefGoogle Scholar
6.Lennox, J. C., On quasinormal subgroups of certain finitely generated groups, Proc. Edinburgh Math. Soc. 26 (1983), 25–28.CrossRefGoogle Scholar
7.Robinson, D. J. S., Finiteness Conditions and Generalized Soluble Groups I (Springer, Berlin 1972).CrossRefGoogle Scholar