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Symmetric group (view source)

Revision as of 22:41, November 24, 2009

500 bytes added ,  22:41, November 24, 2009
hope I described that correctly! - the famous unsolved problem
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A '''symmetric group''' is, simply stated, the collection of all permutations of a set.  This concept has many applications in [[group theory]] of mathematics.
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A '''symmetric group''' is, simply stated, the collection of all permutations of a set.  This concept has many applications in [[group theory]] of mathematics, along with one of its great unsolved problems.
    
==Examples==
 
==Examples==
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In this final arrangement, A has ended up at position 4 (ie, <math>1 \rightarrow 4 \ </math>), D has ended up at position 2, and so on, until we discover the product of the two permutations to be <math>(1427)(35) \ </math>.
 
In this final arrangement, A has ended up at position 4 (ie, <math>1 \rightarrow 4 \ </math>), D has ended up at position 2, and so on, until we discover the product of the two permutations to be <math>(1427)(35) \ </math>.
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== Unsolved Problem ==
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A proposition known as "Netto's conjecture" (proven by Dixon in 1969) states that the probability that two elements P<sub>1</sub> and P<sub>2</sub> of a symmetric group can generate the entire group approaches 3/4 as n increases to infinity.  But a prominent unsolved problem in group theory is to find a general formula for terms in the sequence of a symmetric group.<ref>http://mathworld.wolfram.com/SymmetricGroup.html</ref>
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