Abstract Algebra/Group Theory/Group/Ga = G

From Wikibooks, open books for an open world
Jump to navigation Jump to search

Theorem[edit | edit source]

Let G be any Group.

Let

Proof[edit | edit source]

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 ,