Hw8 Problem 3

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Problem 3

Find all of the left cosets of the subgroup $\langle 3 \rangle$ of $\mathbb{Z_{12}}$.

Solution
$0 + \langle 3 \rangle = \{0, 3, 6, 9\}$

$1 + \langle 3 \rangle = \{1, 4, 7, 10\}$

$2 + \langle 3 \rangle = \{2, 5, 8, 11\}$

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