Let G be a finite group so that every subgroup is normal and has a complement (if H≤ G then there is a K ≤ G with G=H K and H ∩ K= <e>).
a) show that G is abelian
b) for any g ∈G, show o(g) is square free (i.e, a product of distinct primes)
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This is easier if you know about the classification of Dedekind groups (every subgroup is normal). However, it also has a straight forward solution:
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