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Generation of the lower central series II

Published online by Cambridge University Press:  18 May 2009

Robert M. Guralnick
Robert M. Guralnick
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles California 90089-1113, U.S.A.
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In this article, we obtain results on commutators in Sylow subgroups of the lower central series, extending the work of Dark and Newell [2], Rodney [12, 13] and Aschbacher and the author [1, 6, 7].

Some notation is required for the statement of the main results. Let r be a positive integer and define

and

where x1, …, xr, are elements in a group G. Let ΓrG = {[x1, …, xr]∣ x1 ∈ G} be the set of r-fold commutators in G. Then Lr,G = 〈ΓrG〉 is the rth term in the lower central series of G. Set L∞G = ∩ Lr,G.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 25 , Issue 2 , July 1984 , pp. 193 - 201
Copyright
Copyright © Glasgow Mathematical Journal Trust 1984

References

REFERENCES

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