Giventhe group (Z_{24}, +). Consider the subgroup U={ [0]_{24,}[4]_{24,}[8]_{24,}[12]_{24,}[16]_{24,}[20]_{24}}.Determine the elements of Z_{24}/U .
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Originally Posted by uniculdan Giventhe group (Z_{24}, +). Consider the subgroup U={ [0]_{24,}[4]_{24,}[8]_{24,}[12]_{24,}[16]_{24,}[20]_{24}}.Determine the elements of Z_{24}/U . Surely you know that the elements of $\mathbb{Z}_{24}/U$ are just the cosets of $U$ in $\mathbb{Z}_{24}~?$
Originally Posted by Plato Surely you know that the elements of $\mathbb{Z}_{24}/U$ are just the cosets of $U$ in $\mathbb{Z}_{24}~?$ Here is the original text.
Originally Posted by uniculdan Here is the original text. Even from the German, it is not clear to me form of the answer your textbook/instructor wants. Can you give us the element $11+[12]_{24}~?$ Can you give us the coset $11+U~?$
[12]_{24}={...-60, -36, -12, 12, 36, 60,...}. So 11+[12]_{24}={...-49, -25, -1, 33, 47, 71...}=[23]_{24}
Originally Posted by uniculdan [12]_{24}={...-60, -36, -12, 12, 36, 60,...}. So 11+[12]_{24}={...-49, -25, -1, 33, 47, 71...}=[23]_{24} Well done! Now tell us why you cannot finish the exercise?