FTP, name this set with an associative binary operation under which the set is closed and whose best-known type might be the Abelian.
In chemistry, they are used to describe molecular symmetries, and in physics they have led to new particles being discovered.  In math the smallest has order 1, has only the element e, and only the finite simple ones have been classified.  All of them contain an identity element and an inverse for every element in the set, while commutative ones are named after the man who generalized the Binomial Theorem.  FTP, name this set with an associative binary operation under which the set is closed and whose best-known type might be the Abelian.
In chemistry, they are used to describe molecular symmetries, and in physics they have led to new particles being discovered.  
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