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4. Express the following permutations of \{1,2,3,4,5,6\} using cycle notation: $\alpha$ : 1$\mapsto$3, 2$\mapsto$5, 3$\mapsto$6, 4$\mapsto$2, 5$\mapsto$1, 6$\mapsto$4 $\beta$ : 1$\mapsto$2, 2$\mapsto$1, 3$\mapsto$3, 4$\mapsto$6, 5$\mapsto$5, 6$\mapsto$4 $\gamma$ : 1$\mapsto$4, 2$\mapsto$3, 3$\mapsto$6, 4$\mapsto$5, 5$\mapsto$1, 6$\mapsto$2 5. Find the composites $\alpha\beta$, $\alpha\gamma$ and $\beta\gamma$ where $\alpha$, $\beta$ and $\gamma$ are the permutations defined in the previous question. Express the inverses of $\alpha$, $\beta$, $\gamma$ as positive powers of $\alpha$, $\beta$, $\gamma$ respectively.

          4. Express the following permutations of \{1,2,3,4,5,6\} using cycle notation:
$\alpha$ : 1$\mapsto$3, 2$\mapsto$5, 3$\mapsto$6, 4$\mapsto$2, 5$\mapsto$1, 6$\mapsto$4
$\beta$ : 1$\mapsto$2, 2$\mapsto$1, 3$\mapsto$3, 4$\mapsto$6, 5$\mapsto$5, 6$\mapsto$4
$\gamma$ : 1$\mapsto$4, 2$\mapsto$3, 3$\mapsto$6, 4$\mapsto$5, 5$\mapsto$1, 6$\mapsto$2
5. Find the composites $\alpha\beta$, $\alpha\gamma$ and $\beta\gamma$ where $\alpha$, $\beta$ and $\gamma$ are the permutations defined
in the previous question. Express the inverses of $\alpha$, $\beta$, $\gamma$ as positive powers of $\alpha$, $\beta$, $\gamma$
respectively.

4. Express the following permutations of {1,2,3,4,5,6} using cycle notation:
α : 1↦3, 2↦5, 3↦6, 4↦2, 5↦1, 6↦4
β : 1↦2, 2↦1, 3↦3, 4↦6, 5↦5, 6↦4
γ : 1↦4, 2↦3, 3↦6, 4↦5, 5↦1, 6↦2
5. Find the composites αβ, αγ and βγ where α, β and γ are the permutations defined
in the previous question. Express the inverses of α, β, γ as positive powers of α, β, γ
respectively.

Added by Nicole D.

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