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Free subgroups of certain one-relator groups defined by positive words

Published online by Cambridge University Press:  24 October 2008

Gilbert Baumslag
Gilbert Baumslag
Affiliation:
City College of C.U.N.Y., New York
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Extract

Let ℒ be the class of those groups G which can be presented in the form

where u and v are positive words in the given generators. Here a word w is termed positive if only non-negative powers of a, b,…, c occur in w. If each generator occurs with exponent sum zero in uv-1, we term the ℒ-group G a -group. This class contains, in particular, the class X of those groups G which can be presented in the form

where u and v are positive words, and where [u, v] is the commutator uvu-1v-1.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 2 , March 1983 , pp. 247 - 251
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

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