In 1977, I. Prodanov [~ showed that closed subgroups of abellen (q-)mlnlmal topological groups are again (q-) mlnlmsl. These permanence properties do not carry over to the nonabellen case. In fact, in [3J a q-mlnimal topological group X was constructed, containing a nonminlmal closed subgroup G. However, in that example X is not a SIN-group end G is not e normal subgroup of X.In this note we give an example of a q-minimal topological group which is precompact (hence a SIN-group), mstrizeble, but contains a nonminimal closed normal subgroup. This example also gives a negative answer to a problem posed by D.L.
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