# Infinite Groups

Find an infinite group such that every element has finite order.

© BrainMass Inc. brainmass.com October 9, 2019, 3:44 pm ad1c9bdddfhttps://brainmass.com/math/group-theory/infinite-group-elements-12004

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

Find examples of the following: an infinite group such that every element has finite order.

An example is the quotient group Q/Z with the group operation addition "+". We will prove that every element of Q/Z has finite order.

Proof. First of all, the group operation here is addition. Q is the set of rational numbers, Z the set of ...

#### Solution Summary

An infinite group is exemplified, such that every element has finite order

$2.19