Rotman's book *An Introduction to the Theory of Groups* (Fourth Edition) asks, on page 22, Exercise 2.8, to show that S(*n*) cannot be embedded in A(*n*+1), where S(*n*) = the symmetric group on *n* elements, and A(*n*) = the alternating group on *n* elements.  I have a proof but it uses Bertrand's Postulate, which seems a bit much for page 22 of an introductory text.  Does anyone have a more appropriate (i.e., easier) proof?