Let \(\displaystyle \beta = (1 \; 7\; 8)(3 \;10)(6 \;11\; 12)\) in the symmetric group \(\displaystyle S_{12}\)

Express \(\displaystyle \beta\) as a product of transpositions in the form \(\displaystyle (1 \; b)\), with \(\displaystyle b \in \{ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 \}\)

I can express it as normal transpositions, but not sure how to go about it with the first number only being 1.

Thanks

Express \(\displaystyle \beta\) as a product of transpositions in the form \(\displaystyle (1 \; b)\), with \(\displaystyle b \in \{ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 \}\)

I can express it as normal transpositions, but not sure how to go about it with the first number only being 1.

Thanks

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