Hey Piret,
That is the current behavior of EasySocial. If you are a site admin, group admin or a member of a group, you may invite people to the group.
If you want to hack this, you could edit the file /administrator/components/com_easysocial/includes/group/group.php and locate the codes below at line 1679,
[gist]
if ($user->isSiteAdmin() || $this->isAdmin() || $this->isMember()) {
[/gist]
Replace it with,
[gist]
if ($user->isSiteAdmin() || $this->isAdmin()) {
[/gist]
This would only allow site and group admins to invite people. As for events, this can be configured in the settings shown here,
http://take.ms/PYCUE