Unformatted text preview: m i and K = h n i . Find (with proof) a necessary and suﬃcient condition for us to have H ≤ K . Exercise 12. A subgroup H of a group G is called maximal if H 6 = G and whenever we have H ≤ K ≤ G then K = H or K = G (i.e. there are no subgroups “between” H and G ). Use the result of the previous exercise to determine all the maximal subgroups of Z . Exercise 13. Let H i , i ∈ I , be a collection of subgroups of a group G . Prove that K = \ i ∈ I H i is a subgroup of G . Must the union of subgroups also be a subgroup?...
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 Spring '10
 RyanDaileda
 Algebra, Group Theory, Multiplication, Matrices, complex entries

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