$(1 7 3 4)(1 2 3)$ as a product of disjoint cycles and transpositions

Question

I am trying to write $(1 7 3 4)(1 2 3)$ as a product of disjoint cycles and as a product of transpositions

My Attempt: $(1 7 3 4)(1 2 3)= (1 7 3 4)$ as a product of disjoint cycles as $2$ $5$ and $6$ are all fixed values.

$(1 7 3 4)(1 2 3)= (14)(13)(17)$ as a product of transpositions.

I'm not really sure however if $2$ is fixed here. My understanding is that $1$ is sent to $4$, $4$ is sent to $3$, $3$ is sent to $7$ and $7$ is sent to $1$.

I feel that I am misreading this and perhaps $7$ is sent to $2$ and $2$ is sent to $1$

I am aware that this site shouldn't be used to check my work however I really need to improve my understanding of these concepts.

Any help here would be great.

See this post on how to do it. Other duplicates are here or here. — Dietrich Burde, Mar 02 '20 at 19:43
Thanks for your feedback guys, I see my error now. To verify: $3$ and $7$ are interchanged, $1$ is sent to $4$, $4$ is mapped to $2$ and $2$ is mapped to $1$. With the transposition changing to $(1 4)(1 2)(3 7)$ — , Mar 02 '20 at 19:45

score 0 · Accepted Answer · answered Mar 02 '20 at 20:39

0

As stated in the comments, your first step should be to get

$$(1734)(123)=(124)(37),\tag{1}$$

from which you have correctly identified that the RHS of $(1)$ is $(14)(12)(37)$.

answered Mar 02 '20 at 20:39

Shaun

44,997

$(1 7 3 4)(1 2 3)$ as a product of disjoint cycles and transpositions

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