Lecture 24 - Cauchy's theorem

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I'm a bit confused. What is our induction hypothesis here? We showed that for the base case of |G| = 2, the statement is valid. My understanding is that our induction hypothesis should be that the statement is valid for some n and show that it implies the validity of the case |G| = n + 1. But in our induction step, we don't make any reference to |G| in that way.

bibekgautam

Isn't the first case a contradiction, he first assumed that there is no subgroup of order less than G, but in the end he proved otherwise ??

HarshKumar-chss

Construction of Gmod H is of cosets, but construction of group G is of elements originally, how you have considered that Order of Gmod H is less than order of G, let me know, and what is the guarantee that H is of G and, H is non trivial in G, it may be trivial.

tikarambhusal

Sir how to find number of all elements of order for special only non Abelian and Abelian group PLEASE REPLY JAI HIND JAI BHARAT MATA KI JAI

praveshpkofficial

So is it a thrash video?
The only Take away is
1) Prove for base case
2) Prove for some k
3) Prove k implies k+1

So The mistake he made is, he mixed up G and H and also jump of more than 1 ?

revanthkalavala

m should be prime, other wise it is obvious no ex is needed

tikarambhusal

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