Let the group $\Bbb{Z_2} = \{e, a\}$. We are given the quotient group $\Bbb{Z_2} / \{e\}$. So this gives us a set of left cosets: $\Bbb{Z_2} / \{e\} = \{e\{e\}, a\{e\}\} = \{\{e\}, \{a\}\} \neq \{e, a\} = \Bbb Z_2$, but when my professor was explaining solvable groups, he said that $\Bbb{Z_2} / \{e\} = \Bbb{Z_2}$. I don't understand this.
2025-01-13 05:27:51.1736746071
Why is $\Bbb{Z_2} / \{e\} = \Bbb{Z_2}$?
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When he states equality, he actually means that the groups are isomorphic.