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?
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partial cleanup (should “S” and “A” be italicized for uniformity with comments and answers?), [permutation-groups]
An easy proof that S(n) does not embed into A(n+1)?
Len Schrieber
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