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On the “largeness” of one-relator groups

Published online by Cambridge University Press:  20 January 2009

M. Edjvet
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW
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If G is a one-relator group on at least 3 generators, or is a one-relator group with torsion on at least 2 generators, then it follows from results in [1] and [6] that G has a subgroup of finite index which can be mapped homomorphically onto F2, the free group of rank 2. In the language of [2], G is equally as large as F2, written GF2.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1986

References

REFERENCES

1.Baumslag, B. and Pride, S. J., Groups with two more generators than relators, J. London Math. Soc. (2) 17 (1978), 425426.CrossRefGoogle Scholar
2.Edjvet, M. and Pride, S. J., The concept of “largeness” in group theory II, Proc. Conf. on Group Theory, Korea 1983 (Lecture Notes in Mathematics 1098, Springer, Berlin-Heidelberg-New York, 1984).Google Scholar
3.Lyndon, R. C. and Schupp, P. E., Combinatorial Group Theory (Springer, Berlin-Heidelberg-New York, 1977).Google Scholar
4.Pride, S. J., The concept of “largeness” in group theory in Proc. Conf. on Word and Decision Problems in Group Theory and Algebra, Oxford, 1976.Google Scholar
5.Serre, J-P., Trees (Springer, Berlin-Heidelberg-New York, 1980).CrossRefGoogle Scholar
6.Stohr, R., Groups with one more generator than relators, Math. Z. 182 (1983), 45–47.CrossRefGoogle Scholar