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Radical Classes need not have a Unique Maximal R0-Closed Subclass

Published online by Cambridge University Press:  20 November 2018

Roberta Botto Mura
Roberta Botto Mura*
Affiliation:
University of Alberta, Edmonton
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It was shown in [1] that certain classes of groups which are closed under quotients, and extensions contain a unique maximal inclosed subclass. These results prompted the question whether there exists a class of groups which is closed under quotients and extensions and yet does not have a unique maximal R0-closed subclass. This note provides an example of such a class.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 4 , 01 December 1974 , pp. 597 - 598
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Rex, Dark and Rhemtulla, Akbar H., On RQ-closed classes, and finitely generated groups. 1970 Can. J. Math. Vol. XXII, pp. 176-184.Google Scholar
2. Robinson, Derek J. S., Finiteness conditions and generalized soluble groups. Part 1. Springer- Verlag 1972.Google Scholar