Lagrange's Theorem -- Abstract Algebra 10

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[Zebinify]

There might be a typo at 46:03? should it be (h^k)*g = g*h^(P-k)?

[lexinwonderland]

Great lecture!! I'm particularly glad you mentioned a matrix group at the end to connect with the seemingly abstract finite groups, it really helps tie it together and feel like "math" to a newcomer.

I really wish you'd pointed out the (most?) canonical isomorphism between GL2(Z2) and D3, especially noting that [0, 1;1, 0] is very similar to the identity but a "flip"... hmm, makes you think of the element s in a dihedral group...

[matheusjahnke]

at 4:50
fi(h)=gi * h=left[gi](h) for all h in H
except we know left[gi] is a member of SG(he showed that before*)... so it is bijective at G.... if you create an fi with an adequately restrained domain and codomain.... you create another bijective function fi.

[dewookus]

This video and the entire course are fantastic. One question though: Looking at the board at time 46:53, I wonder if one could just go directly from the observation that G is the disjoint union of H and gH to the line where the elements of G are listed. We know the h^k's are all distinct since the order of h is p, and we can see the g(h^k)'s are distiinct by the cancellation law for groups. That gives us all of G, as desired.
Thanks,
Dave

[aashsyed]

19:34 we will look at in a previous video

[visheshlonial]

hello can anyone please help me understand how to prove the result at 45:30. I can't seem to figure it out myself