TITLE: Examples of Infinite Simple Groups
QUESTION [12 upvotes]: I would like a list of infinite simple groups. I am only aware of $A_\infty$.
Any example is welcome, but I'm particularly interested in examples of infinite fields and values of $n$ such that $PSL_n(F)$ is simple.
References about this topic, or any example, are also appreciated.

REPLY [3 votes]: Here is the list of examples we have which were directed by the comments thus far:

$PSL_n(K)$ for when $K$ is an infinite field and $n\geq 2$ 1
The finitary alternating group $A(\kappa)$ for any infinite cardinal $\kappa$ 2

REFERENCES

This entry at Groupprops shows that $PSL_n(K)$ is actually simple for all $n\geq 2$ and any $K$ except for $PSL_2(\Bbb F_2)$ and $PSL_2(\Bbb F_3)$
This question addresses this fact