3rd Isomorphism Theorem

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This 3rd Isomorphism Theorem can be intuitively understood as:

G partitioned by a bigger normal subgroup H
is isomorphic to:
{G partitioned by a smaller normal subgroup K (which is a subgroup of H)}
partitioned by
{H partitioned by a smaller normal subgroup K}

or, by ‘abuse of arithmetic’: divide G & H by a common factor K.

(G / H  ) =  (G / K ) / (H / K )

Analogy:
$100 / $50 = 2 (two $50 notes makes $100)
is same (isomorphic) as
$100 / $10 = 10, (ten $10 notes makes $100)
$50/$10 = 5, (five $10 notes makes $50)
then 10/5 = 2 (ten notes split into five is two )

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