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 homomorphism with ker(\Phi) = H
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 homomorphism with ker(\Phi) = H
