Did you check to see if "User authentication for NetWorker" is enabled on NMC? All users by default have monitor permission so what would be the reason to give them special group?

i think you misunderstood.
Here is the situation:
We assign a group of personnel in the department that will monitor all the systems via monitoring screens and their duties are;
- to monitor system back-ups and logs.
- not to enable/disable scheduled groups autostart property.
- can stop running back-ups when necessary.

Can we create a user having these permissions?

Obviously to stop NW groups you need more than monitor privilege and that one might include other things as you already noticed.

I also tried it now - and something is broken big time. I used 7.4SP2, create dummy user which was not listed anywhere in admin group and was able to do all sort of bad things including deleting volumes. It seems as bug (I didn't test it with nsrauth enabled, but I do not recall that being requirement) and you should report it to support.

i have just create a default user and i can able to start and stop a group. The user is also not in the administrators group. just a default user with monitor privilege

Funny enough, it happens only with NMC and backup server are installed on the same box... at least in my test case.

in my case, i did the things from my desktop using NMC.

I did that too, but the NMC is package is installed on the same box as backup server.

If I install the NMC package on another server, will the problem be solved? is a dummy user still can start/stop a group or not?

Yes, installing it on remote server addresses the issue.