Find a subgroup of S4 which contains six elements. How many subgroups of order six are there in S4?

Find the order of each of the following elements in the multiplicative group of units . for for for for

Exercises 19. Find cyclic subgroups of that have three different orders.

Let n be appositive integer, n1. Prove by induction that the set of transpositions (1,2),(1,3),...,(1,n) generates the entire group Sn.