# Answer on Abstract Algebra Question for Jasvinder Singh

Question #44356

5) a) Let H = h(1 2)i and K = h(1 2 3)i be subroups of S3. Check that S3 = HK. Is S3 the internal

direct product of H and K? Justify your answer.

b) Let s = 1 2 3 4 5 6 7

2 4 5 6 7 3 1and t = 1 2 3 4 5 6 7

3 2 4 1 6 5 7be elements of S7.

i) Write both s and t as product of disjoint cycles and as a product of transpositions,

ii) Find the signatures of s and t.

iii) Compute ts

direct product of H and K? Justify your answer.

b) Let s = 1 2 3 4 5 6 7

2 4 5 6 7 3 1and t = 1 2 3 4 5 6 7

3 2 4 1 6 5 7be elements of S7.

i) Write both s and t as product of disjoint cycles and as a product of transpositions,

ii) Find the signatures of s and t.

iii) Compute ts

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