English Dictionary

semidirect product

名詞

(group theory) 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.

日本語の意味

群論において、直積の一般化。2つの部分群のうち、片側のみが正規部分群となるという条件のもとで形成される積の構造。 / 直積の構造に類似しながら、一方の部分群だけが正規性を持つ点で区別される群の合成方法。

The symmetry group of the wallpaper pattern can be described as a semidirect product of a translation subgroup and a point group.

その壁紙模様の対称群は、平行移動部分群と点群の半直積として表現できる。

意味（1）

(group theory) 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 […] .

semidirect products （ plural ）