models.rb

class User < ActiveRecord::Base
  has_many :groups, through: :group_users
end

class GroupUsers < ActiveRecord::Base
  belongs_to :user
  belongs_to :group
end

class Group < ActiveRecord::Base
  has_many :users, through: :group_users
end

So you're saying:
A group belongs to a single user. That user owns the group.
In addition, a user may belong to any number of groups - but not own it?
And a Group has many users - some of which may belong to other groups or own other groups?

Can a user own multiple groups?

Um... yeah kind of.

A group belongs to a single user yes, that user owns that group.
In addition, a user may belong to any number of groups and not own them. For instance another user might add them to their own group which they would not own.

And a group can have many users.

edit: And yes a user could have multiple groups.

class User < ActiveRecord::Base
  has_and_belongs_to_many :groups
  has_many :owned_groups, class_name: :Group
end

class Group < ActiveRecord::Base
  has_and_belongs_to_many :users
  belongs_to :owner, class_name: :User
end