Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $(a_1,a_2,\cdots,a_n) \in G_1 \oplus \cdots \oplus G_n$. Give a necessary and sufficient condition for $|(a_1,a_2,\dots,a_n)| = \infty$.

I think if one $a_i$ has order $\infty$, then this would give a necessary condition. It is sufficient for the order of the direct product to be $\infty$ when only one of the $a_i$ has order $\infty$?

Thanks,

share|improve this question

1 Answer 1

up vote 2 down vote accepted

The order of $(a_{1},a_{2}, \cdots , a_{n}) \in \oplus_{i} G_{i}$ is the least common multiple of the orders of the $a_{i} \in G_i$, so it is bounded by the product of the orders. Does this help you answer your question?

share|improve this answer
    
So, if one of a_i has order $\infty$, we are done. is that correct? –  Marvin Gaye Sep 23 '12 at 21:23
    
That is correct. –  Isaac Solomon Sep 23 '12 at 21:24

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.