Geodesic
Radical Classes need not have a Unique Maximal R 0-Closed Subclass
Canadian mathematical bulletin, Tome 17 (1974) no. 4, pp. 597-598

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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. 
Mura, Roberta Botto. Radical Classes need not have a Unique Maximal R 0-Closed Subclass. Canadian mathematical bulletin, Tome 17 (1974) no. 4, pp. 597-598. doi: 10.4153/CMB-1974-107-7
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[1] 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] 2. Robinson, Derek J. S., Finiteness conditions and generalized soluble groups. Part 1. Springer- Verlag 1972. Google Scholar

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