1. Answer the following questions briefly. No justiļ¬cation is needed for (a), (b), (c). (a) List an order 7 element in S7.

(b) List two order 8 groups which are not isomorphic to each other. (c) List elements of a subgroup of S4 which is isomorphic to the group of symmetries of

a regular triangle. (d) Explain why there is no element of order 7 in A6. (e) Explain why all groups of order 5 are isomorphic to one another. (f) If (1 2 4)g(5 3 2) = (3 6 5 4) for some 9 in 5’6, calculate g and simplify it into a

product of disjoint cycles. Math