Opposite group

In group theory, a branch of mathematics, an opposite group is a way to construct a group from another group that allows one to define right action as a special case of left action.

Let ${\displaystyle G}$ be a group under the operation ${\displaystyle *}$. The opposite group of ${\displaystyle G}$, denoted ${\displaystyle G^{\mathrm {op} }}$, has the same underlying set as ${\displaystyle G}$, and its group operation ${\displaystyle {\mathbin {\ast '}}}$ is defined by ${\displaystyle g_{1}{\mathbin {\ast '}}g_{2}=g_{2}*g_{1}}$.

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