Group Theory | Sylow Theorem | Sylow First Theorem - Proof and Example

[@donebis8703]

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🙏🙏🙏

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[@swastiktiwari7066]

I think some corrections are needed in slides at 9:39 and 9:59 : O(H) = p , so when p^m divides O(G) and you re-write O(G) as O(G)/O(H)*O(H) , this means p^m divides O(G)/O(H)*p => p^(m-1) divides O(G)/O(H) => p^(m-1) divides order O(G/H) of quotient group G/H

[@dragonmanialegendsindia]

10:27 sir par theorem me to bola Gaya h ki p^m se divisible hoga to p^m+1 se divisible nahi hoga ppane p^m-1 liya h jabki wo p^m se bhi divisible h ..... Kese sir please explain

[@joshkanungo195]

Nice explanation on First Sylow's theorem Sir.

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Mujhe to kuch samajh nahi aaya 😢😢😢

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[@skyressgo]

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[@odxshobhityt527]

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[@Billonaire_saga1.0]

Sir in this proof in place of N(a) [Normalizer of a] you should use C(a)[centralizer of a] because normalizer is defined for a subgroup not for an
You are an outstanding teacher ❤❤❤❤

[@faheemhamzafaheemhamza1874]

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[@abhaypetkar357]

00:11 Sylow's theorem is important for competitive exams and includes three theorems
00:59 Sylow's First Theorem: Group has at least one subgroup with order equal to a prime number
03:09 Sylow's theorem explains the existence of subgroups in a group based on prime orders
04:48 Sylow's first theorem can be proven by induction
05:36 Sylow First Theorem states that any group has at least one subgroup whose order is a prime power.
06:33 Prime number divides order of G implies there exists an element
08:16 The Sylow First Theorem explains the existence of normal subgroups in a group.
10:58 Sylow's First Theorem states that a group with prime power as a divisor of its order will have at least one subgroup of prime power order.

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Cauchy theorem bhi kra do

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Exam ke liye please sir

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topic ko khtm krne ki kosis mt kiya karo sir ,
Ek topix ko axe se pdao sir taaki sb clear ho jaye,
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Please sir,Sylow's I and II theorem proof par videos banaeye.

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Sir in sylow first theorem statemenr p ki power n+1 doesn't divide O(G) will not use

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sir why induction is a hypothesis?
As we use it everywhere.

[@Tushar-pg2em]

Is it because of its axiomatic nature ?

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Sir in Sylow first theorem there is also a role of normal subgroup. But you are not discussing it

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At 1.12
Kindly check.

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sir can you pls provide sylow 1st theorem proof pdf without induction method 🥺🥺🥺🥺🥺

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Prove that for any group G, |G/Z(G)|≠91

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