Can't read a file although it's in my group and permissions for group read are set

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http://unix.stackexchange.com – I encounter a strange problem on a unix/linux machine: I'm member of a group, let's call it group A and a certain file (which has a different owner) belongs to group A as well. The permissions of that file are -rw-rw---- so I'd expect I should be able to open that file, but I am not: I'll get the "Permission denied" error message when I try to look at the file's content (using cat). Since the permissions seem to be correct, what else could be causing this? Are there "overriding" permission restrictions in place? If so, how would I find out? (HowTos)