Phrase guide

semidirect product

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

Each Play button uses your device's default local English voice, or a natural local fallback. The selected voice name appears after playback. This is synthesized speech, not a source recording.

No pronunciation record was provided for this word.

1

noun

Meaning 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.

Definition source: English Wiktionary via Wiktextract

Topics: group-theory, mathematics, sciences

Examples

  • 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 [...] .

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

Refers to the fact that the criteria are less strict than for the direct product; compare semidirect.