Can S5 contain a subgroup of order 7?

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Discussion Overview

The discussion centers on whether the symmetric group S5 can contain a subgroup of order 7, exploring implications of group theory and Lagrange's theorem.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant asserts that S5 can contain a subgroup of order 7.
  • Another participant references Lagrange's theorem as relevant to the question.
  • A question is raised regarding the order of S5 and its divisibility by 7.
  • A subsequent reply states that 7 does not divide the order of S5, which is 120.

Areas of Agreement / Disagreement

Participants express differing views on the possibility of S5 containing a subgroup of order 7, with some referencing mathematical principles that suggest it cannot.

eileen6a
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not homework question and i say yes.
 
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Lagrange's theorem answers this question
 
What is the order of S5? Is that divisible by 7?
 
No as 7 does not divide 5! = 120.
 

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