# What is subgroup $\langle g^d \rangle$?

According to the introductory abstract algebra, it says that $g^n =e$ where $g$ is an element of some finite group. Then, it talks about the subgroup $\langle g^d \rangle$. What is it exactly, and what would be the elements of this group? (where $d$ is some integer.)

-
@William modified $n$ to $d$. –  Lucy Zeo Aug 18 '12 at 1:20

The notation $\langle g^d \rangle$ denotes the cyclic group generated by the element $g^d$. More explicitly, we begin with the element $g^d$. Then we consider $g^d \cdot g^d = g^{2d}$. We continue generating more elements of the subgroup and have the set $\{g^d, g^{2d}, g^{3d}, \cdots\}$ with the group operation coming from the finite group.