Abstract Algebra/Group Theory/Group/Ga = G

Theorem

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Let G be any Group.

Let  

 

Proof

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Part A.  

0. Choose  
1. Choose  
2.  
1.
3.  
closure of G,  
4.  
2,

Part B.  

5. Choose  
6.  
definition of inverse
7. Choose  
8.  
closure of G, and, y, a−1 are in G
9.  
definition of Ga
10.  
associativity on G (not Ga)
11.  
eG is identity of G
12.  

Part C.  

 
  and  ,