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We can look at the group action of H on G/H (through left multiplication). H is a subgroup of N(H). Suppose H=N(H). then we can have only one orbit of size 1 (ie orbit of H). By class equation p^t= 1 +sigma p^(t-k) where (as G is a p group so would its subgroups ie stabilizers). If t=0 or n then its just N(H)=G else then 0<k<t<n which is not possible
Your explanation is great but i think it will difficult to understand for those who doesn't have the idea about poset specifically the 3 crucial relationship regarding partial order relation
I tried to send you a private message, but didnt succeed. So, I'm posting here. I don't speak Hindi, so please pardon me if you said it and I missed it. In your first slide, one need not even consider the case where W1 and W2 are disjoint. If each of W1 and W2 is a subspace of a parent vector space, say V, then they cannot possibly be disjoint---they must share the zero element in V. Warm regards.
Thankyou mam 😊 but keep in memory that you are recording video for us (for student) and if writing such important theorem then please mam 😢 conside to explain the theorem so that we can understant the theorem.
Maam, R is an ED implies that R is an ID as well, then by def it will have unity, since ID is a commutative ring with unity without zero divisors.14:45??
