Timeline for Multiplicative and additive groups of the field $(\prod_{n\in\omega}\mathbb{Z}/p_n\mathbb{Z})/\simeq_{\cal U}$
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 24, 2020 at 10:37 | comment | added | Sean Eberhard | Yes you are right, my mistake, thanks. | |
| Jul 24, 2020 at 10:33 | comment | added | Emil Jeřábek | Homomorphisms do not preserve the order of elements. A preimage of an element of order $n$ may have order $mn$, or even infinite. | |
| Jul 24, 2020 at 10:12 | comment | added | Sean Eberhard | If every $p_n$ is a Fermat prime then $(\mathbb{Z}/p_n\mathbb{Z})^\times \cong \mathbb{Z}/2^{k_n}\mathbb{Z}$, so $K^\times$ contains a unique element of order 2, and it has a square root, so there is no epimorphism $K^\times \to \mathbb{R}^\times$. | |
| Jul 24, 2020 at 9:58 | history | answered | Sean Eberhard | CC BY-SA 4.0 |