9. Order of an Element | Order of Group | Order of an Element of Group

Order of an element: - (A, *) be a group, then ∀ a ∈ A, order of a is denoted by O(a),
O(a) = smallest positive Let integer n, such that
a^n = e

• order of identity element is always one


• order of an element and its inverse is always same


• order of an element in an infinite group does not exist or infinite expect identity

Order of group: - order of a group is denoted by O(G) = no of elements in G

• Group with a single element must be an identity element

Order of an Element,Order of Group,