Unformatted text preview: H a . Hence H a is a subgroup. Hint for 6.48 . Every group is a union of its cyclic subgroups, because every element that generates a cyclic group contains that element. None of these cyclic subgroups can be inﬁnite, because otherwise it would be isomorphic to ( Z , +)....
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 Spring '08
 OGUS
 Math, Algebra, Subgroup, Cyclic group, cyclic subgroups

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