Without listing the elements of the left cosets, determine if (123)//= (132)//fo

Question

Without listing the elements of the left cosets, determine if (123)//= (132)//for the subgroup H = {e, (12)} in (S_3,o). Without listing the elements of the left cosets, determine if 4 + H = 7 + H for the subgroup H = {0,3,6,9} in (Z12, +i2). W'ithout listing the elements of the left cosets, determine if 7//= 5H for the subgroup H = {1,8} in (U(9), Without listing the elements of the left cosets, determine if 3 + H = 9 + H for the subgroup H = {0,5,10,15} in (Z_20, +20). Use Lagrange's Theorem to determine the possible subgroup sizes in a group with exactly 40 elements.

Explanation / Answer

17) NO not the same

18) No not the same

19) NO not the same/

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