semidirect product

Etymology
Refers to the fact that the criteria are less strict than for the ; compare.

Noun

 * 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.
 * 2) * 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 (editors), Geometry of Differential Equations,, Translations, Series 2, Volume 186, Advances in the Mathematical Sciences 39, page 8,
 * The preceding result is a special case of a general theorem on reduction by stages for semidirect products acting on a symplectic manifold.

Usage notes
Two equivalent mathematical definitions exist, which, for didactic purposes, are sometimes distinguished as inner semidirect product and outer semidirect product.