In both British and American English, if you are using initial (i.e. first) letters to represent words, you don’t normally need to put a full stop after them. Example BBC, UK, NATO
In American English, it is common to use a full stop as an alternative style for certain** abbreviations. Example USA and U.S.A. both are right abbreviation for "United State of America"
PE is abbreviation of Physical Education.
PE is more formal and correct without dots(.)