Let G be an abelian group and let H and K be finite cyclic subgroups with |H|
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Let G be an abelian group and let H and K be finite cyclic subgroups with |H| = r and |K| = s.
a. Show that if r and s are relatively prime, then G contains a cyclic subgroup of order rs.
b. Generalizing part (a), show that G contains a cyclic subgroup of order the least common multiple of r and s.
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a Let a be a generator of H and let b be a generator of K Because G is abelian we have ab rs a r ...View the full answer
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