Each user different category

I recently installed Drupal, v. 4.6.3, and I'm quite pleased with it.
But I was wondering if it was possible for me to let each user edit only 1 certain node.
I am running a site for different groups, and I want each group to get access to their own page, where they can edit their content.
Is this possible? I want to limit the users to only edit their page. Nothing more. How can this be done? Should I create user groups or something?
Thanks for any answers.