Dicyclic Group - Generalizations

Generalizations

Let A be an abelian group, having a specific element y in A with order 2. A group G is called a generalized dicyclic group, written as Dic(A, y), if it is generated by A and an additional element x, and in addition we have that = 2, x2 = y, and for all a in A, x−1ax = a−1.

Since for a cyclic group of even order, there is always a unique element of order 2, we can see that dicyclic groups are just a specific type of generalized dicyclic group.