Definition:Group Action on Coset Space
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Definition
Let $G$ be a group.
Let $H$ be a subgroup of $G$.
The mapping $*: G \times G / H \to G / H$ by the rule:
- $\forall g \in G, \forall g' H \in G / H: g * \paren {g' H} := \paren {g g'} H$
is the group action on the (left) coset space $G / H$.
Also see
- Results about the group action on a coset space can be found here.
Sources
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): Chapter $6$: Cosets: Exercise $9$
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: The Sylow Theorems: $\S 53$