So when a group acts on a set faithfully means that the action is a one to one correspondence? To me this is reminiscent of kernels of group homomorphisms f for which f^{-1}(e')={e}.
@cpaniaguam That is exactly the idea. The action defines a homomorphism of the group into the symmetry group of the set. Faithful means one-one, so we are identifying the group with a subgroup of symmetries. Otherwise we have some quotient of the group as a subgroup of symmetries.
Worth the reminder: each g in the group acts the set as a one-one correspondence. - Bob
So when a group acts on a set faithfully means that the action is a one to one correspondence? To me this is reminiscent of kernels of group homomorphisms f for which f^{-1}(e')={e}.
cpaniaguam 5 months ago
@cpaniaguam That is exactly the idea. The action defines a homomorphism of the group into the symmetry group of the set. Faithful means one-one, so we are identifying the group with a subgroup of symmetries. Otherwise we have some quotient of the group as a subgroup of symmetries.
Worth the reminder: each g in the group acts the set as a one-one correspondence. - Bob
MathDoctorBob 5 months ago
Thank you! You've done a good job!
YesITMarketing 5 months ago
@YesITMarketing You're welcome! - Bob
MathDoctorBob 5 months ago
Gr8!
Your lecture is so clear that we just need to take it once!
Brazilian universities need Algebra Teachers like you!
One question: is this stick for dummies????
dfnmartins 6 months ago
@dfnmartins Thanks! I'd love to visit Brazil. No sticks for dummies, just for pointing. - Bob
MathDoctorBob 6 months ago
@ 4:38 is where the real fun begins
identification21 10 months ago