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Answer the following questions briefly. No justication is needed for (a), (b), (c). (a) List an order 7 element in S7. (b) List two order 8 groups...
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.