EXTENDED GENUS OF TORSION-FREE FINITELY GENERATED NILPOTENT GROUPS OFCLASS-2

The extended genus of a nilpotent group N is the set of isomorphism cl asses of nilpotent groups M, not necessarily finitely generated, such that the p-localizations M(p), N-p, are isomorphic for all primes p. I n this article, for any torsion-free finitely generated nilpotent grou p N of nilpotency class 2, the extended genus of N is analyzed by assi gning to each of its members a sequence of triads of matrices with rat ional entries, generalizing the sequential representation which has be en exploited elsewhere in the case when N is abelian. This approach al lows, among other things, to obtain examples of groups in the ordinary (Mislin) genus of N.