Let G be a group of order 150 = 2 × 3 × 52. Assume N G with |N| = 6. Prove that N is the only. subgroup of order 6 in G. Hint: Draw a diagram, and use a proof by contradiction.
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Let G be a group of order 150 = 2 × 3 × 52. Assume N G with |N| = 6. Prove that N is the only. subgroup of order 6 in G. Hint: Draw a diagram, and use a proof by contradiction.
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- If a is an element of order m in a group G and ak=e, prove that m divides k.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.Let H be a subgroup of the group G. Prove that the index of H in G is the number of distinct right cosets of H in G.
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