1. Answer the following questions briefly. No justification is needed for (a), (b), (c). (a)List an order

1. Answer the following questions briefly. No justification 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 g in S6, calculate g and simplify it into a product of disjoint cycles. 

1. Answer the following questions briefly. No justification 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 ofa 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 aproduct of disjoint cycles.