Definition:Opposite Group
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Theorem
Let $\struct {G, \circ}$ be a group.
We define a new operation $*$ on $G$ by:
- $\forall a, b \in G: a * b = b \circ a$
The algebraic structure $\struct {G, *}$ is called the opposite group to $G$.
Also see
- Opposite Group is Group, demonstrating that this is indeed a group
- Definition:Group Antihomomorphism
- Definition:Opposite Ring
- Results about opposite groups can be found here.
Sources
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: The Definition of Group Structure: $\S 26 \epsilon$