Assertion: abelian group | /r/HasProperty | divisible
Facets:
value: for every prime p
type: TEMPORAL
Source sentences:
text: An abelian group ( G , + ) {\displaystyle (G,+)} is divisible if, for every positive integer n {\displaystyle n} and every g ∈ G {\displaystyle g\in G} , there exists y ∈ G {\displaystyle y\in G} such that n y = g {\displaystyle ny=g} .
text: An Abelian group is called complete, or divisible, if for any one of its elements $a$ and for any integer $m$ the equation $mx=a$ has a solution in the group.
text: A third equivalent condition is that an abelian group G {\displaystyle G} is divisible if and only if G {\displaystyle G} is an injective object in the category of abelian groups; for this reason, a divisible group is sometimes called an injective group.
text: An abelian group is divisible if and only if it is p -divisible for every prime p .
text: An Abelian group is divisible if and only if, regarded as