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Exam (elaborations)
MATH 425 Exam 3
MATH 425 Exam 3 
Group Closed, Associative, Identity, Inverse 
One-to-one If f(x)=f(y), then x=y 
Onto For any element in the codomain, there is an element in the domain that maps to it 
Homomorphism Function that satisfies the property upphi(xy) = upphi(x) upphi(y) 
Isomorphism Homomorphism Property, One-to-one, Onto 
Kernel Set of all elements in the domain that map to the identity in the codomain 
Factor Group Thm: Let Phi : G xrightarrow{}[] G' be a group homom...