Group Theory · Algebra
Homomorphisms and Isomorphism Theorems
The First Isomorphism Theorem is the fundamental duality: quotienting by the kernel is the same as taking the image. These theorems are the main tools for classifying groups.
WHAT STUDENTS WILL LEARN
✓Define homomorphisms; identify kernel and image
✓Prove the First Isomorphism Theorem: G/kerφ ≅ imφ
✓Apply the Second and Third Isomorphism Theorems
✓Classify small groups up to isomorphism
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