[math-fun] uniquely factored groups

JHC> The only candidate for an isomorphism that these invariants leave is between 2xQ8 and 4 :^3 4, which is prohibited by the unique factorisation theorem for direct products, since it's easy to see that the latter of these two isn't a non-trivial direct product. John, could you state precisely the unique factorization theorem? I've never seen it written down. There seem to be some subtleties, such as checking that AxB = AxC implies B=C. (For groups, of course, we interpret "=" as isomorphism.) Is it also true for infinite groups? Rich