Yes, from backend configuration of GJ under the Groups tab simply set Create to Disabled. This won't affect you as a Super Admin though so you'll still be able to create groups from frontend. Additionally the Category owner can also create groups in their categories so you may want to limit this as well (see Category tab).

thank you for your answer. how can i set that only me can create groups in a category or only me can create categories.

I've already explained this, please read my previous reply.

i have no group create entry in my frontend. how can i set it ?

You need to be viewing GJs frontend, not the tab on your profile. You can find the frontend by clicking the Frontend URL (at the top above the navigation icons) in GJs backend panel.

more importent; is there a group search form. so that users can search for groups ?

Yes, everything is search capable, display count capable, and paging capable. When navigating to a category users are able to search the groups within that category.

like choosing a category and get a list of all groups of this category?

Yes, this is how it functions.

Searching is doable from frontend, you need to navigate to a category on frontend and you can search its list of groups. This assumes you have no disabled searching in GJ configuration in backend. The frontend of GJ is found by using the Frontend URL on the Plugin page when navigating to GJ from Plugin Management in the backend. Click the link and it will take you to frontend.