Determination of groups of prime-power order

Of course the general problem can be solved in principle. For instance one could write down all Latin squares of a given order, check which can be regarded as tables for associative multiplications and then test for isomorphisms. What one wants are practical methods. I won't here go into all the methods that have been proposed or used. Let me just sketch, very briefly, results obtained for the case of prime-power orders. Cayley himself had already settled the case of prime order in 1854. Metro (1882) settled squares of primes; Young (1893) and H~ider (1893), independentl~settled cubes and fourth powers. Bagnera (1898) essentially settled

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