Abstract Algebra - Isomorphism

  • Thread starter jz0101
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  • #1
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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!!
 

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  • #2
haruspex
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What, in words, does S42 represent?
 
  • #3
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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).
 
  • #4
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@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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