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Abstract Algebra - Isomorphism

  1. Feb 26, 2014 #1
    1. Show that S42 contains multiple subgroups that are isomorphic to S41.
    Choose one such subgroup H and find σ1,....,σ42 such that



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    How can you solve this?? I am confused if anyone can help me to solve this!!
     
  2. jcsd
  3. Feb 26, 2014 #2

    haruspex

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    What, in words, does S42 represent?
     
  4. Feb 26, 2014 #3
    I'll assume you already identified a subgroup ##H## that is isomorphic to ##S_{41}##. Think about the cosets of ##H##. How many are there? (If this is a hard question, try looking over a proof of Lagrange's Theorem).
     
  5. Feb 26, 2014 #4
    @kduna: I am studying by myself reading book. Now I saw this question which I wanted to know how to solve this question.
     
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