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Let f be a homomorphism from group G to group K.
Let eK be identity of K.
- is a subgroup of K.
0.
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homomorphism maps identity to identity
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1.
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0. and
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- 2. Choose ||
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- 3.
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2.
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- 4.
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i is in K and eK is identity of K(usage3)
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5.
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2, 3, and 4.
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6. is identity of
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definition of identity(usage 4)
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0. Choose |
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- 1.
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0.
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- 2.
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homomorphism maps inverse to inverse between G and K
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- 3.
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homomorphism maps inverse to inverse
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- 4. i has inverse f( k-1) in im f
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2, 3, and eK is identity of im f
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5. Every element of im f has an inverse.
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0. Choose |
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- 1.
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0.
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- 2.
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Closure in G
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- 3.
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- 4.
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f is a homomorphism, 0.
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- 5.
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3. and 4.
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0. im f is a subset of K |
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1. is associative in K |
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2. is associative in im f |
1 and 2
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