semidirect products

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...