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Generating groups of certain soluble varieties

Published online by Cambridge University Press:  09 April 2009

Narain Gupta  and
Frank Levin
Narain Gupta
Affiliation:
University of Manitoba, Winnipeg, Canada
Frank Levin
Affiliation:
Rutgers, The State University, New Brunswick, N. J., U. S. A. and Ruhr Universität, Bochum, W. Germany.
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Any variety of groups is generated by its free group of countably infinite rank. A problem that appears in various forms in Hanna Neumann's book [7] (see, for intance, sections 2.4, 2.5, 3.5, 3.6) is that of determining if a given variety B can be generated by Fk(B), one of its free groups of finite rank; and if so, if Fn(B) is residually a k-generator group for all n ≧ k. (Here, as in the sequel, all unexplained notation follows [7].)

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 17 , Issue 2 , March 1974 , pp. 222 - 233
Copyright
Copyright © Australian Mathematical Society 1974

References

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