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Soluble groups in which every finitely generated subgroup is finitely presented

Published online by Cambridge University Press:  09 April 2009

J. R. J. Groves
J. R. J. Groves
Affiliation:
University of MelbourneParkville, Victoria 3052Australia
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Abstract

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The class of finitely generated soluble coherent groups is considered. It is shown that these groups have the maximal condition on normal subgroups and can be characterized in a number of ways. In particular, they are precisely the class of finitely generated soluble groups G with the property:

Subject classification (Amer. Math. Soc. (MOS) 1970): primary 20 E 15; secondary 20 F 05.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 1 , August 1978 , pp. 115 - 125
Copyright
Copyright © Australian Mathematical Society 1978

References

Artin, Emil (1968), Algebraic Numbers and Algebraic Functions (Nelson, London).Google Scholar
Baumslag, Gilbert (1973), “Subgroups of finitely presented metabelian groups”, J. Austral. Math. Soc. 16, 98–110.CrossRefGoogle Scholar
Baumslag, Gilbert (1974), “Finitely presented metabelian groups”, Proc. Second Internat. Conf. Theory of Groups,Calberra,1973, pp. 65–74 (Lecture Notes in Mathematics 372, Springer-Verlag, Berlin, Heidelberg, New York).CrossRefGoogle Scholar
Bieri, Robert and Strebel, Ralph (to appear), “Almost finitely presented soluble groups”.Google Scholar
Robinson, Derek J. S. (1972), Finiteness Conditions and Generalized Soluble Groups, Parts 1 and 2 (Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 62, 63. Springer-Verlag, Berlin, Heidelberg, New York, 1972).CrossRefGoogle Scholar
Wehrfritz, B. A. F. (1973), Infinite Linear Groups (Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 76. Springer-Verlag, Berlin, Heidelberg, New York).CrossRefGoogle Scholar