Groups available in different site collections

Is it possible that I create a group that is available to assign permission to, under different site collections ?

You may not be able to create a group avaialable in multiple site collections.

The nearest possible option is - you can set User Policy on a web application which would allow you to set the following permission types in all its site collections.

•  Full Control - Has full control.
•  Full Read - Has full read-only access.
•  Deny Write - Has no write access.
•  Deny All - Has no access.

You can select individual AD users / AD security groups as part of setting up web app user policy from Central Admin...