Don't have developed core strength for L-Sits.

What are some exercises gymnast use to get unbelievable core strength?

I don't have rings right now they broke so I must buy new onces.

So I can only use the ground for now.

This progression should help to get you started:

http://gymnasticbodies.com/forum/viewtopic.php?t=634

Yours in Fitness,

Coach Sommer

They don't work any of the normal core strength you see anywhere else, their core strength comes from skills. But I would work on V-ups to help with the hips, core and those tiny quad. muscles that will help you with the L-sit. I would also work these, I'm not sure of the name but I'll do my best to describe them, sit in the piked position, then place your hands near your knees, and lift your legs while your hands are still on the floor. Its a simple workout, if you need more description I'll be glad to take pictures.