Abstract Algebra/Group Theory/Group/Ga = G

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Theorem[edit]

Let G be any Group.

Let

Proof[edit]

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 ,