Let K and H be subgroups of a finite group G with KCHCG.lf [G:K] = 12 and [H:K] = 3. Then, [G:H] = Оз О 12 4 O None of the choices O 48
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![Let K and H be subgroups of a finite group G with KCHCG. If [G:K] = 12 and [H:K] =
3. Then, [G:H] =
12
O 4
None of the choices
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- 10. Suppose that and are subgroups of the abelian group such that . If is a subgroup of such that , prove that .Let H be a subgroup of the group G. Prove that if two right cosets Ha and Hb are not disjoint, then Ha=Hb. That is, the distinct right cosets of H in G form a partition of G.24. Let be a group and its center. Prove or disprove that if is in, then and are in.