`comm -1 -3` (http://pubs.opengroup.org/onlinepubs/9699919799/utilities/co...) is practically made for quickly finding who is a member of all involved groups.
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There are a couple of differences between comm and join:
comm compares whole lines; join compares fields within lines.
comm prints whole lines; join can print selected parts of lines.
http://stackoverflow.com/questions/7234028/bash-difference-b...