Are there independent research groups?

I wanted to ask if someone knows how to find independent researchers or research groups. I mean, people interested in doing Math in a research level that are not related to universities neither investigation institutes, that freely choose and propose research topics and discuss their own results, with the purpose of (maybe) writing a publishable paper.

Thanks,

Dan

Added comment: For independently I mean that for example some guy is interested in lets say p-adic numbers. So he begins to study them independently and finds some new publishable results. By independent research group I mean a group of guys (not necessarily in the same place or country) interested in lets say, p-adic numbers that share comments and results via email and eventually get a publishable paper. They are independent in the sense that they do not do research in what an entity (university, at&t, etc.) Tells them, but in a topic they share common interest.

Solution 1:

One possible place to look might be the National Coalition of Independent Scholars (NCIS) http://www.ncis.org/