问一个抽代题

annimalUID: 2616512

Suppose H and K are two subgroups of a group G, and that the orders of H and K are 12 and 30 respectively. Which of the following cannot be the order of the subgroup of G generated by H and K, and why?

A. 30
B. 60
C. 120
D. 360
E. Countably infinite

我主要是不明白由H和K生成的子群是什么意思。。是H中任意拿一个，然后K中任意拿一个，做群的运算得到的集合吗？这样的集合好像有可能连子群都不是。。

annimalUID: 2616512

明白了。。。包含H 和 K的最小子群

druiseUID: 3001059

选B吧

treemantanUID: 2770681

druise 发表于 2012-10-28 13:10
选B吧

A。。。This new group M is generated by H and K, which are two subgroups. So H is a subgroup of M and then the order of H divides M. So is the order of K. Thus, the order of M is at least 60 which is the lcm(H,K). Probably Wrong.HHA

druiseUID: 3001059

treemantan 发表于 2012-10-29 21:24
A。。。This new group M is generated by H and K, which are two subgroups. So H is a subgroup of M  ...

看着A打成B我能乱说?郁闷
不过谢谢了,好心人啊