Semidirect product
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English
Etymology
Refers to the fact that the criteria are less strict than for the Template:M; compare Template:M.
Noun
- Template:Label 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.
- 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, Template:W, 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 manifoldTemplate:....
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- Template:Quote-book
- 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, Template:W, Translations, Series 2, Volume 186, Advances in the Mathematical Sciences 39, page 8,
Usage notes
Two equivalent mathematical definitions exist, which, for didactic purposes, are sometimes distinguished as inner semidirect product and outer semidirect product.