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As a transformation of alphabets, this is the (1-E)-transform, where E is the exponential alphabet, whose elementary symmetric functions are e_n=1/n!. In the case of noncommutative symmetric functions, we recover Schocker's idempotents for derangement numbers [Discr. Math. 269 (2003), 239].\n  From these idempotents, we construct subalgebras of the descent algebras analogous to the peak algebras and study their representation theory. 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