Math and science::Algebra::Aluffi

# 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 $$g$$.