semidirect product

Noun

semidirect product (plural semidirect products)

1. A generalisation of direct product such that, in one of two equivalent definitions, only one of the subgroups involved is required to be a normal subgroup.
   • The preceding result is a special case of a general theorem on reduction by stages for semidirect products acting on a symplectic manifold […] .1998, Hernán Cendra, Darryl D. Holm, Jerrold E. Marsden, Tudor S. Ratiu, Lagrangian Reduction, the Euler-Poincaré Equations, and Semidirect Products, A. G. Khovanskiĭ, A. Varchenko, V. Vassiliev...
   • Also, by Lemma 3.1, every group G with a normal subgroup N and complement H is isomorphic to a semidirect product of N by H, and so once we prove Theorem 3.2, it will be fair to say that we have constructed all possible split extensions (up to isomorphism).2008, I. Martin Isaacs, Finite Group Theory, American Mathematical Society, page 69