一类多重循环群的剩余有限性质

On the Residual Finiteness of a Class of Polycyclic Groups

设A是秩为n(n≥2)的自由Abel群,A的自同构群Aut(A)=GL(n,Z).对整数m,取α=(010…000┆┆┆┆┆┆┆000…0110…0 m)记∈Aut(A).记Г_(m)(n)=A×<α>则它是一个2元生成的多重循环群.本文给出了Γ_(m)(n)的准确的剩余有限性质.

Let A be a free Abelian group of rank n(n≥2).For a rational integer m,takeα=(010…000┆┆┆┆┆┆┆000…0110…0 m)∈Aut(A).LetΓ_(m)(n)i=A×<α>,thenΓ_(m)(n)is a polycyclic group generated by two elements.In this paper,the residually finiteness ofΓ_(m)(n)is analyzed.