?? "prime decomposition for actions of g" ... ????..... "classification" .... ???.
(briefly mention analogy to, as well as prime numbers, (finite ... ??? ...) groups themselves ... ??? ....)
??possibly tying in with suggested homework exercise ... ???... finding all the subgroups ... ???...
??at some point possibly combinatorial counting applications of this sort of stuff ... ???? ....
??also bit about example of 4-elt set ...
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