semidirect product
Word Rarity
Very rare
Frequency: Zipf frequency 1.03 in modern English
27
Scrabble Score
17
Letters
4
Syllables
11
Unique Chars
Meaning
noun
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.
Example Sentences
- "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, American Mathematical Society, 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 […] ."
- "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)."
- "Theorem 4.8.5 Let G be a group, H,Klt;G,H◅ G. Then G is the internal semidirect product of H and K if and only if H#92;capK#61;1 and G#61;HK. Many groups can be understood as semidirect products."
Etymology
Refers to the fact that the criteria are less strict than for the direct product; compare semidirect.