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semidirect product

A generalization of the direct product where H's action on N (by conjugation) may be non-trivial -- the direct product is the special case where the action is trivial.

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Examples

  • D_n itself is a semidirect product \mathbb{Z}_n \rtimes \mathbb{Z}_2, since a reflection's conjugation action on a rotation is non-trivial -- it inverts it.

See also

internal direct product dihedral group
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