Determine the order of the coset containing each of the following elements in the respective quotient...

Question

Question

Determine the order of the coset containing each of the following elements in the respective quotient groups.

order element quotient group (6,1) Z16 Z18/((4, 13)) (9, 11) Z12 Z18/((6, 13)) (4,3) Z10 U(10)/((6, 7)) (12,9) Z14 * U(14)/{(

Answer 1

Answer #1

® We know that order 19, b) = com [orderela), orderlts] So 0 16,1) eis 2164 218 214, 13) » = Lem( 3, 13) = 39 ② (9,11) in Zia

Answer 2

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