undergraduate math about permutation
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for example: Let f : G −→ H denote an isomorphism between the two
groups G,H.
(a) For any g ∈ G show that order(g)=order(f(g)).
(b) G is abelian iff H is abelian.
(c) G is cyclic iff H is cyclic.
(d) G and H have the same number of elements
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