finitely generated group

例句：

1. 1.The finitely generated group is a mathematical concept that has been studied for centuries.
   有限生成群是一个数学概念，已经被研究了几个世纪。
2. 2.Infinitely generated groups are particularly interesting because they can be used to generate infinite sequences of numbers.
   无限生成群特别有趣，因为它们可以用来生成无限的数字序列。
3. 3. Finitely generated groups have applications in cryptography and computer science, where they are used to secure data and prevent unauthorized access.
   有限生成群在密码学和计算机科学中有应用，它们被用来保护数据并防止未经授权的访问。