PlanetMath (more info)
 Math for the people, by the people. Sponsor PlanetMath
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
Owner confidence rating: Very high Entry average rating: Very high
divisible group (Definition)

An abelian group $D$ is said to be divisible if for any $x\in D$ , $n\in\Z^+$ , there exists an element $x'\in D$ such that $nx'=x$ .

Some noteworthy facts:




"divisible group" is owned by mathcam.
(view preamble | get metadata)

View style:


Attachments:
example of divisible group (Example) by mathcam
$n$-divisible group (Definition) by CWoo
abelian group is divisible if and only if it is an injective object (Theorem) by joking
Log in to rate this entry.
(view current ratings)

Cross-references: cardinal number, rationals, torsion subgroup, direct sum, subgroup, isomorphic, group, divisible, abelian group
There are 6 references to this entry.

This is version 4 of divisible group, born on 2003-07-23, modified 2003-07-24.
Object id is 4499, canonical name is DivisibleGroup.
Accessed 3614 times total.

Classification:
AMS MSC20K99 (Group theory and generalizations :: Abelian groups :: Miscellaneous)

Pending Errata and Addenda
None.
[ View all 2 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)