|
3 | added 1 characters in body | ||
|
In the finitely generated case it follows by the structure theorem that the unique possibilities are $G=\mathbb{Z}$ and $G=\mathbb{Z}/({p_1}^{e_1})\oplus \mathbb{Z}/({p_2}^{e_2})\oplus\cdots\oplus \mathbb{Z}/({p_k}^{e_k})$, where $p_1,\dots,p_k$ are distinct primes. Edit: in a word, the unique possibility is that $G$ is cyclic, as remarked by Jack Schmidt below. |
||||
|
|
2 | added 104 characters in body | ||
|
In the finitely generated case it follows by the structure theorem that the unique possibilities are $G=\mathbb{Z}$ and $G=\mathbb{Z}/({p_1}^{e_1})\oplus \mathbb{Z}/({p_2}^{e_2})\oplus\cdots\oplus \mathbb{Z}/({p_k}^{e_k})$, where $p_1,\dots,p_k$ are distinct primes. Edit: in a word the unique possibility is that $G$ is cyclic, as remarked by Jack Schmidt below. |
||||
|
|
1 |
|
||
|
In the finitely generated case it follows by the structure theorem that the unique possibilities are $G=\mathbb{Z}$ and $G=\mathbb{Z}/({p_1}^{e_1})\oplus \mathbb{Z}/({p_2}^{e_2})\oplus\cdots\oplus \mathbb{Z}/({p_k}^{e_k})$, where $p_1,\dots,p_k$ are distinct primes. |
||||
