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On R0-Closed Classes, and Finitely Generated Groups

Published online by Cambridge University Press:  20 November 2018

Rex Dark  and
Akbar H. Rhemtulla
Rex Dark
Affiliation:
Kings College, Cambridge, England
Akbar H. Rhemtulla
Affiliation:
University of Alberta, Edmonton, Alberta
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1.1. If a group satisfies the maximal condition for normal subgroups, then all its central factors are necessarily finitely generated. In [2], Hall asked whether there exist finitely generated soluble groups which do not satisfy the maximal condition for normal subgroups but all of whose central factors are finitely generated. We shall answer this question in the affirmative. We shall also construct a finitely generated group all of whose subnormal subgroups are perfect (and which therefore has no non-trivial central factors), but which does not satisfy the maximal condition for normal subgroups. Related to these examples is the question of which classes of finitely generated groups satisfy the maximal condition for normal subgroups. A characterization of such classes has been obtained by Hall, and we shall include his result as our first theorem.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 1 , 01 February 1970 , pp. 176 - 184
Copyright
Copyright © Canadian Mathematical Society 1970

References

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