Simple group is that it is not trivial and subgroups of simple group must be improper and trivial.
So, every simple abelian group has trivial subgroup and improper subgroup.
So, I think center of every simple abelian group is trivial subgroup and abelian group itself.
But, My professor says that the center of every simple abelian group is improper subgroup, whole group itself.
So, I am confused whether trivial subgroup of simple abelian group is center or not.
Best Answer
In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself. Now centre of a group is normal. Now for an abelian group the center of the group is the group itself. So, there is no confusion!!