Question regarding group theory

Reference no: EM13125623

1. Prove that the subgroup of A4 generated by any element of order 2 and and any element of order 3 is all of A4.

2. Prove that if x and y are distinct 3-cycles in S4 with x != y^-1 (x not equal to the inverse of y), then the subgroup of S4 generated by x and y is all of A4.

Reference no: EM13125623

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Question regarding group theory : Prove that the subgroup of A4 generated by any element of order 2 and and any element of order 3 is all of A4. Prove that if x and y are distinct 3-cycles in S4 with x != y^-1 (x not equal to the inverse of y), then the subgroup of S4 generated by x..

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