Find the elementary divisors and invariant factors

[fabiancillo]

Hello I have problems with this exercise

Find the elementary divisors and invariant factors of each of the following groups

a) $G1= Z_6 \times Z_{12} \times Z_{18}$ , b) $G_2= Z_{10} \times Z_{20} \times Z_{30} \times Z_{40}$Thanks

 

[fabiancillo]

a) I think that elementary divisors are $\{2,3,2^2,3,2,3^2 \} $ because is the prime decomposition of ${6,12,18}$.

b) elementary divisors are $\{5 ,2 ,2^2, 5, 2, 3, 5, 2^3, 5 \}$
. But I don't use the Chinese remainder theorem to split each factor into cyclic pp-groups, then regroup

 

[Euge]

You are correct so far in parts (a) and (b). You just need to find the invariant factors now.