Dictionary entry
mathematical group
数学群：一个集合及其上的二元运算，满足封闭性、结合律、单位元和逆元。
A set together with a binary operation satisfying closure, associativity, identity, and invertibility.
- 1.
a set that is closed, associative, has an identity element and every element has an inverse
In use
In abstract algebra, a mathematical group is a set with an operation that combines any two elements to form a third.
The set of integers with addition forms a simple mathematical group.
Every mathematical group must satisfy the properties of closure, associativity, identity, and invertibility.
a + mathematical group + verb phrase
作为主语，描述定义。
A mathematical group is a set together with an operation that satisfies four axioms.
数学群是一个集合及其上满足四条公理的运算。
the + mathematical group + of + noun phrase
指定具体群，常后接 of 短语说明元素。
We consider the mathematical group of integers under addition.
我们考虑整数加法下的数学群。
in + a/the + mathematical group
表示在群内讨论性质。
In a mathematical group, every element has an inverse.
在数学群中，每个元素都有逆元。
the order of + a/the + mathematical group
表示群的阶这一概念。
The order of a mathematical group is the number of elements it contains.
数学群的阶是它所包含的元素个数。
Common mistakes
这个集合是一个数学组。这个集合是一个数学群。
汉语中“数学组”通常指一个团队或部门，而代数结构“mathematical group”应译为“数学群”。
数学群具有结合性。数学群满足结合律。
结合性不是标准的数学术语，应使用“结合律”来表述运算的封闭性质。
Connections
Dictionary facts from ECDICT, WORDNET.