I have a Group 'g1' having 2 users Alice and Bob. I want to share a file 'file1' with both of them with different permissions.(for Alice read only and for Bob Read+write)
Assuming Bob can own the file the following should work for you.
$ chown Bob:g1 file1
First set the ownership of the file to Bob to allow for read+write access and set the group ownership to the g1 group.
$ chmod 640 file1
Set the owner to a read and write and set the group to read only. This is a common permission structure on webservers. Note that the "world" has no permissions in this structure, but $ man chmod can provide further information on file permissions and get you where you are needing to go. Additionally if you need more control over your permissions across the whole system you may want to look into Posix ACLs or SE Linux as you did indicate you are on RedHat