Confirming the Order of Permutation: LCM = 8

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Discussion Overview

The discussion revolves around determining the order of a permutation expressed as the product of two cycles, specifically (1 2 3 4) (1 2 3 4). Participants are examining the calculation of the least common multiple (LCM) of the orders of these cycles and whether the initial claim of the order being 8 is correct.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant claims that the order of the permutation is LCM = (4, 4) = 8.
  • Another participant challenges this claim, stating that LCM(4, 4) is not 8 and suggests double-checking the math.
  • A later reply confirms that the order of the permutation is indeed the LCM of the orders of each cycle but also indicates that the correct LCM is 4.
  • Another participant advises checking the method for finding the order and references the importance of expressing permutations in disjoint cycles to determine the order correctly.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as there are competing views regarding the correct calculation of the order of the permutation and the interpretation of the LCM.

Contextual Notes

There are unresolved mathematical steps regarding the calculation of the LCM and the method for determining the order of permutations, particularly in relation to cycle notation.

WM07
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Can you tell me if my answer is correct?

in (1 2 3 4) (1 2 3 4) The order of permutation is LCM = (4, 4) = 8
 
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WM07 said:
Can you tell me if my answer is correct?

in (1 2 3 4) (1 2 3 4) The order of permutation is LCM = (4, 4) = 8

The order of the permutation is indeed the LCM of the order of each. However, you may want to double check your math. LCM(4,4) is not 8.

:-)
 
rs1n said:
The order of the permutation is indeed the LCM of the order of each. However, you may want to double check your math. LCM(4,4) is not 8.

:-)


Thank you, I get the least common multiple is 4 am I right?
 

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