The following are definitions commonly used when discussing mathematical groups.
- Order of a Group - denoted {% |G| %} is the number of elements of the group.
- Order of an Element - the order of an element {% g %} is the smallest number {% n %} such that {% g^n = e %}. That is {% g %} multiplied by itself {% n %} times is equal to the identity of the group. (here we call the group operation multiplication)
- Center of a Group
- the center of a group, {% Z(G) %} is the set of elements {% z \in G %}
such that {% z %} commutes with every element of G.
That is
{% Z(G) = \{ z\in G | zx = xz for all x \in G \} %}