711: m-Cycle on n-Symmetric Group

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definition of m-cycle on n-symmetric group

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Topics

About: group

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Structured Description
• 2: Natural Language Description

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Starting Context

• The reader knows a definition of n-symmetric group.

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Target Context

• The reader will have a definition of m-cycle on n-symmetric group.

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Orientation

There is a list of definitions discussed so far in this site.

There is a list of propositions discussed so far in this site.

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Main Body

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1: Structured Description

Here is the rules of Structured Description.

Entities:
$n$: $\in \mathbb{N}\setminus \{0\}$
$S_n$: $=\text{ the }n\text{ -symmetric group }$
$m$: $\in \mathbb{N}\setminus \{0\}$ such that $m\le n$
$\{p_1,...,p_m\}$: $\subseteq S_n$ with any order of the elements
$\ast (p_1,...,p_m)$: $\in S_n$
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Conditions: $(p_1,...,p_m):p_1\mapsto p_2,...,p_{m-1}\mapsto p_m,p_m\mapsto p_1$ with every other element mapped to itself
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2: Natural Language Description

For any natural number, $n\in \mathbb{N}\setminus \{0\}$, the $n$-symmetric group, $S_n$, any natural number, $m\in \mathbb{N}\setminus \{0\}$ such that $m\le n$, and any subset, $\{p_1,...,p_m\}\subseteq S_n$, with any order of the elements, $(p_1,...,p_m)\in S_n$ such that $(p_1,...,p_m):p_1\mapsto p_2,...,p_{m-1}\mapsto p_m,p_m\mapsto p_1$ with every other element mapped to itself

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References

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