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Abstract Algebra

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Moderate

Embedding of $S_3$ in $S_6$

ABSALG-1IEDQN

Associate the elements of $S_3$ with the elements $1,\ldots, 6$ as follows:

$1 \leftrightarrow 1, (12) \leftrightarrow 2, (13) \leftrightarrow 3, (23) \leftrightarrow 4, (123) \leftrightarrow 5, (132) \leftrightarrow 6$.

Given this association, what is the image of $(12) \in S_3$ under the embedding $S_3 \hookrightarrow S_6$ coming from the action of $S_3$ on itself by left multiplication?

A

$(12)$

B

$(12)(35)(46)$

C

$(13)(25)(46)$

D

$(16)$

E

$(12)(56)$

F

$(13)(46)$