Abstract Algebra - Isomorphism

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Homework Help Overview

The discussion revolves around the properties of the symmetric group S42 and its subgroups, specifically focusing on identifying subgroups isomorphic to S41. The original poster expresses confusion regarding the problem and seeks assistance in understanding how to approach it.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the representation of S42 and consider the identification of a subgroup H isomorphic to S41. There is a suggestion to think about the cosets of H and the implications of Lagrange's Theorem.

Discussion Status

The discussion is ongoing, with participants exploring different aspects of the problem. Some guidance has been offered regarding the consideration of cosets and the application of Lagrange's Theorem, but no consensus or resolution has been reached yet.

Contextual Notes

The original poster indicates they are studying independently and are looking for clarification on the problem without specific instructions on how to solve it.

jz0101
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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


MIDpro4.png



How can you solve this?? I am confused if anyone can help me to solve this!
 
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What, in words, does S42 represent?
 
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).
 
@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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