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Group Theory Proof

  • Thread starter HuaYongLi
  • Start date
  • #1
16
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Homework Statement


G is a commutative group, prove that the elements of order 2 and the identity element e form a subgroup.


Homework Equations





The Attempt at a Solution


I don't know where to even begin.
 

Answers and Replies

  • #2
352
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Given any subset [tex]H \subset G[/tex], how would you attempt to prove that it is a subgroup of [tex]G[/tex]? What properties of [tex]H[/tex] would you attempt to verify?
 
  • #3
16
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Well I guess associativity, unique inverse and identity element are all trivial.
What I'm having trouble with is closure, proving that for any elements a and b in the group, ab is also in the group.
 
  • #4
2,967
5
You need to prove that if a and b are elements of order 2 (i.e. [itex]a^{2} = b^{2} = e[/itex]), then so is [itex]c = a b[/itex]. You need to evaluate [itex]c^{2}[/itex] and use the commutativity of the group.
 
  • #5
16
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Thank You
 

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