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Generation of the lower central series

Published online by Cambridge University Press:  18 May 2009

Robert M. Guralnick
Robert M. Guralnick
Affiliation:
University of Southern California, Los Angeles, California 90007
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Let G be a group. The rth term LrG of the lower central series of G is the subgroup generated by the r-fold commutators

where , and for r > 1,

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 23 , Issue 1 , January 1982 , pp. 15 - 20
Copyright
Copyright © Glasgow Mathematical Journal Trust 1982

References

REFERENCES

1.Dark, R. S. and Newell, M. L., On conditions for commutators to form a subgroup, J. London Math. Soc. (2) 17 (1978), 251–262. (Reviewed in Zbl. Math. 388 (1979), 102).CrossRefGoogle Scholar
2.Gallagher, P. X., The generation of the lower central series, Canad. J. Math. 17 (1965), 405–410.CrossRefGoogle Scholar
3.Gordon, B., Guralnick, R., and Miller, M., On cyclic commutator subgroups, Aequationes Math. 17 (1978), 241–249Google Scholar
4.Guralnick, R., On cyclic commutator subgroups, Aequationes Math., 21 (1980), 33–38.Google Scholar
5., Guralnick, R., Commutators and commutator subgroups, Advances in Math. (to appear).Google Scholar
6.Liebeck, H., A test for commutators, Glasgow Math. J. 17 (1976), 31–36.Google Scholar
7.MacDonald, I. D., On cyclic commutator subgroups, J. London Math. Soc. 38 (1963), 419–422.CrossRefGoogle Scholar
8.Rodney, D. M., On cyclic derived subgroups, J. London Math. Soc. (2) 8 (1974), 642–646.CrossRefGoogle Scholar
9.Scott, W. R., Group theory (Prentice-Hall, 1964).Google Scholar