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Handout Monday 10/13
Recall that a subset of a group that is itself a group (using the same operation as the original group) is called a subgroup . We have described subgroups in two ways so far:
Listing the elements of the subgroup. For example,
\(\{r_0, r_2, f_1, f_2\}\text{.}\)
Giving a condition that elements in the subgroup must satisfy. For example,
\(\{g \in G \st g^2 = e\}\text{.}\)
Today we will consider a third way: The smallest subgroup that contains one or more particular elements.
