Introduction. In [6] Mislin defined the genus (JV) of a finitely generated nilpotent group N as the set of isomorphism classes of finitely generated nilpotent groups M such that for all primes p the p-localizations of M and N are isomorphic, that is Mp Np for all primes p. If the isomorphism class of M belongs to @(N), we say that M e <&(N). Moreover if N e JfQ, that is, N is a finitely generated infinite nilpotent group with a finite commutator subgroup [N,N], then Hilton and Mislin ([4]) showed that (N) has the structure of a finite abelian group. For the reader's convenience, we gather in the first section the definitions and results that we will need.
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机译:介绍。在[6]中,Mislin将有限生成的幂等子群N的属(JV)定义为有限生成的幂等子群M的同构类的集合,这样对于所有素数p,M和N的p局部都是同构的,即Mp所有素数的Np p。如果M的同构类属于@(N),则说M e <&(N)。此外,如果N e JfQ,即N是带有有限换向子子集[N,N]的有限生成的无限幂群,则Hilton和Mislin([4])表明(N)具有有限阿贝尔群的结构。 。为了方便读者,我们在第一部分中收集了我们需要的定义和结果。
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