Groups. All orders divides order of maximal element
Order: divides order of maximal element
Let \( G \) be a [something] group, and let \( g \in G \) be an element with maximal finite order. Any other element with finite order has an order that [has what relationship?].
The same statement cannot be made for non-comutative groups.
Can you remember the proof?
Maximal finite order
Let \( g \) be an element of group \( G \). \( g \) has maximal finite order iff all other elements with finite order have an order less than that of \( g \).