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Recall that Sn is the group consisting of the set of all bijections from 1, 2, ..., n to 1, 2, ..., n together with the binary operation ◦ denoting composition of functions. (a) Find a cyclic subgroup of S4 that has two elements. (b) Find a cyclic subgroup of S4 that has three elements. (c) Find a cyclic subgroup of S4 that has four elements. (d) Find a subgroup of S4 that is isomorphic to (Z2 × Z2, ), and prove that the two groups are isomorphic.
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