Every user is normally alone in a group with the same name, $USER if that user is executing the command. $george is the content of the shell variable george, an empty string if that variable is not defined. However, the command did the right thing because, according to 'info chown':

OWNER‘:’
     If a colon but no group name follows OWNER, that user is made the
     owner of the files and the group of the files is changed to OWNER’s
     login group.

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