411 REFERENCE · Wikibooks
Abstract Algebra/Group Theory/Group/Ga = G
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Theorem
Let G be any Group.
Let
Proof
Part A.
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|0. Choose
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1. Choose
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2.
|| 1.
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3.
|| closure of G,
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4.
|| 2,
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Part B.
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| 5. Choose
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6.
|| definition of inverse
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7. Choose
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8.
|| closure of G, and, y, a−1 are in G
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9.
|| definition of Ga
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10.
|| associativity on G (not Ga)
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11.
|| eG is identity of G
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12.
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Part C.
and ,