Linked server issue

As part of security we have implemented groups and removed the individual logins from server and database.

but for linked servers access we are unable to add those groups. here if we are creating individual logins then only we can able to execute the linked server queries.

how can we add the groups to linked servers.we doesn't want to create individual logins.

EXEC sp_addlinkedsrvlogin 'servername', 'false', 'domainusername', 'login', 'password'

i have executed the above query this is also creating the individual logins.
also in the security tab if we choose 4 th option using sa password we can able to execute. but with this login all the users can able to execute the linked server queries. here we want only specific people should execute the linked queries.

please help me out from this.