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Katie Holmes is keeping Suri active amid all the divorce drama ...

Katie's divorce from Tom Cruise was finalized this week, making it one of the quickest turnarounds in Hollywood celebrity split history.

Meanwhile, the separation has got to be taking its toll on only child Suri. It appears Katie's keeping her daughter active and social, but encouraging her to meet new kids at the park and to integrate with other boys and girls her age. Suri has long been somewhat isolated by being out of school and with private tutors, taking private ballet lessons and staying unusually close to her mother.

Suri did make a friend today at the park -- the two rode the slide, compared notes about their bicycles ... hey, they were probably even discussing the Lance Armstrong debate! But whatever the girls talked about, little Suri looked as happy as we've seen her in a while ... until it was time to go!