Group Theory (Abstract Algebra) question! o(G) vs o(g)??

Question

If G is a group, and g is an element of G, what is the difference between the following two notations o(G) and o(g)?

Answer 1

Typically $$o(g)=\min\{n\in\mathbb{N}:\,g^n=e\}$$ is the order of the element $g$, whereas $$o(G)=\sum_{x\in G}{1}$$ is the number of elements in the group $G$ as a whole.

Answer 2

$o(g)$ is the order of the element, which is the size of the cyclic subgroup generated by the element. Although the notation $|G|$ is more typical, $o(G)$ almost certainly means the order of the group. In general $o(g)$ divides $o(G)$ for any $g \in G$.