Galois groups of unramified extensions over maximal cyclotomic fields

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Let K be the field obtained by adjoining all roots of unity to the rationals. We have strengthened our previous result on unramified Galois extensions of K having non-solvable Galois groups. The result is as follows. There exists an unramified Galois extension of K having the direct product of countable number of copies of SL2(Zp) as the Galois group, p being any prime greater than 3.