Is 2a=0 a Subgroup of an Abelian Group?

[kathrynag]

Homework Statement

Let G be an abelian group such that the operation on G is denoted additively. Show that 2a=0 is a subgroup on G. Compute this subgroup for G=Z12.

Homework Equations

The Attempt at a Solution

Well, I started out by knowing that abelian means ab=ba.

 

[Mark44]

Homework Statement

Let G be an abelian group such that the operation on G is denoted additively. Show that 2a=0 is a subgroup on G. Compute this subgroup for G=Z12.

Homework Equations

The Attempt at a Solution

Well, I started out by knowing that abelian means ab=ba.

The problem should probably be stated like this. Show that the set {a | 2a = 0} is a subgroup of an abelian group G.

Since the operation is addition, abelian means a + b = b + a.