# Changes

## Quasicyclic group

, 02:11, 11 August 2012
| [[satisfies property::p-group]] || Yes || || Hence, it is an [[satisfies property::abelian p-group]], so also a [[satisfies property::nilpotent p-group]].
|}

==Related notions==

===Combining quasicyclic groups for all primes===

The [[restricted external direct product]] of the $p$-quasicyclic groups for all prime numbers $p$ is isomorphic to $\mathbb{Q}/\mathbb{Z}$, the [[group of rational numbers modulo integers]].

The [[additive group of p-adic integers]] can, in a vague sense, be considered to be constructed using a method dual to the method used to the [[quasicyclic group]]. While the $p$-adics are constructed as an inverse limit for surjective maps $\mathbb{Z}/p^n\mathbb{Z} \to \mathbb{Z}/p^{n-1}\mathbb{Z}$, the quasicyclic group is constructed as a direct limit for injective maps $\mathbb{Z}/p^{n-1}\mathbb{Z} \to \mathbb{Z}/p^n\mathbb{Z}$.