[代數] abelian group/isomorphism個數

[star66 (star)]

在A First Course in Abstract Algebra這本書裡的Chapter11,
講到了Finitely Generated Abelian Groups。
該節裡有個習題是,
how many abelian groups, up to isomorphic, are of order 24? 25? 24*25?

藉由Finitely Generated Abelian Groups,
there are 3 abelian groups of order 24
2 abelian groups of order 25,
然後因為24和25互質，
由定理Zn x Zm isomorphic to Znm if gcd(m,n)=1,
there are 2*3=6 abelian groups of order 24*25.

不知道這樣的思路是不是正確的呢？

另外一個想釐清的問題是，
如果是16*18, 兩個不互質的數，就必須把16*18做質因數分解，
16*18=2^5*3^2, 用Finitely Generated Abelian Groups求解囉？

謝謝大家幫忙~~

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