Translation guide
A coset is a mathematical concept from group theory. In Japanese, it is expressed using the technical term 剰余類 (じょうよるい). This guide explains how to refer to cosets in mathematical contexts.
The mathematical concept of a coset: a subset formed by multiplying all elements of a subgroup by a fixed element of the group.
The standard Japanese term for 'coset' in group theory. Used in textbooks and academic papers.
To specify left or right coset, use 左剰余類 (ひだりじょうよるい) and 右剰余類 (みぎじょうよるい).
When the left coset and right coset coincide, the subgroup is a normal subgroup.
Choose a representative element of the coset.
The loanword 'coset' written in katakana. Sometimes used in informal or spoken mathematical discussions, but less common than 剰余類.
The order of this coset is equal to the order of the subgroup.