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Subgroups of finitely presented metabelian groups

Published online by Cambridge University Press:  09 April 2009

Gilbert Baumslag
Gilbert Baumslag
Affiliation:
Rice University, Houston, Texas, U. S. A.
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In 1961 Graham Higman [1] proved that a finitely generated group is a subgroup of a finitely presented group if, and only if, it is recursively presented. Therefore a finitely generated metabelian group can be embedded in a finitely presented group.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 1 , August 1973 , pp. 98 - 110
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Higman, G., ‘Subgroups of finitely presented groups’, Proc. Roy. Soc. London Ser. A 262 (1961), 455–475.Google Scholar
[2]Hall, P., ‘Finiteness conditions for soluble groups’, Proc. London Math. Soc. (3) 4 (1954), 419–436. MR 17, 344.Google Scholar
[3]Baumslag, G., ‘A finitely presented metabelian group with a free abelian derived group of infinite rank’, Proc. Amer. Math. Soc. 35 (1972), 61–62.Google Scholar
[4]Magnus, W., ‘On a theorem of Marshall Hall’, Ann. Math. 40 (1939), 764–768.CrossRefGoogle Scholar
[5]Atiyah, M. F. and Macdonald, I. G., Introduction to commutative algebra (Addison-Wesley, 1969) ME 30 ≠ 4129.Google Scholar