Definition:Inner Semidirect Product
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Definition
Let $G$ be a group.
Let $H$ be a subgroup of $G$.
Let $N$ be a normal subgroup of $G$.
Let $H$ and $N$ be complementary.
Then $G$ is the inner semidirect product of $N$ and $H$.
This is denoted $G = N \rtimes H$ or $G = H \ltimes N$.
Also see
Sources
- 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{II}$: Groups: Problem $\text{DD}$