| dbo:abstract |
In group theory, a field of mathematics, a double coset is a collection of group elements which are equivalent under the symmetries coming from two subgroups. More precisely, let G be a group, and let H and K be subgroups. Let H act on G by left multiplication and let K act on G by right multiplication. For each x in G, the (H, K)-double coset of x is the set When H = K, this is called the H-double coset of x. Equivalently, HxK is the equivalence class of x under the equivalence relation x ~ y if and only if there exist h in H and k in K such that hxk = y. The set of all double cosets is denoted by (en) 군론에서 이중 잉여류(二重剩餘類, 영어: double coset)는 주어진 두 부분군에 의하여 결정되는 동치 관계에 대한 동치류이다. (ko) 在数学领域, 群G中的 (H,K) 双陪集在G上的等价关系下是一个等价类, 其中 H K 是 G 的子群, G上的等价关系定义如下 x ~ y, 如果存在 h 属于 H , k 属于 K 满足 hxk = y. 每个双陪集具有形式 HxK, 并且 G 分割为自身的 (H, K) 双陪集; 双陪集中的每个元素, 都是 H 在 G 中的右陪集 Hy和 K 在 G 中的左陪集 zK 的组合. 一类重要的情形是 H = K, 这时有一类内积 HyH·HyH 是双陪集的一个并集. 在某些材料中, 例如有限群, 这可以作为相关的环的基. (zh) |
| rdfs:comment |
군론에서 이중 잉여류(二重剩餘類, 영어: double coset)는 주어진 두 부분군에 의하여 결정되는 동치 관계에 대한 동치류이다. (ko) 在数学领域, 群G中的 (H,K) 双陪集在G上的等价关系下是一个等价类, 其中 H K 是 G 的子群, G上的等价关系定义如下 x ~ y, 如果存在 h 属于 H , k 属于 K 满足 hxk = y. 每个双陪集具有形式 HxK, 并且 G 分割为自身的 (H, K) 双陪集; 双陪集中的每个元素, 都是 H 在 G 中的右陪集 Hy和 K 在 G 中的左陪集 zK 的组合. 一类重要的情形是 H = K, 这时有一类内积 HyH·HyH 是双陪集的一个并集. 在某些材料中, 例如有限群, 这可以作为相关的环的基. (zh) In group theory, a field of mathematics, a double coset is a collection of group elements which are equivalent under the symmetries coming from two subgroups. More precisely, let G be a group, and let H and K be subgroups. Let H act on G by left multiplication and let K act on G by right multiplication. For each x in G, the (H, K)-double coset of x is the set When H = K, this is called the H-double coset of x. Equivalently, HxK is the equivalence class of x under the equivalence relation x ~ y if and only if there exist h in H and k in K such that hxk = y. (en) |
