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

[@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

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[@amankumarbehera6232]

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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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[@khemrajchaulagai6855]

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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 ❤❤❤❤

[@highermathematics-bx4mi]

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Please sir,Sylow's I and II theorem proof par videos banaeye.

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Nice explanation on First Sylow's theorem Sir.

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[@garimamishra6890]

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

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[@arijitmajumder2638]

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[@MMMtalks-nu4mc]

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

[@Tushar-pg2em]

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

[@Tushar-pg2em]

Is it because of its axiomatic nature ?

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

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𝗦𝗶𝗿 𝗽𝗹𝗲𝗮𝘀𝗲 𝗺𝗮𝗸𝗲 𝘃𝗶𝗱𝗲𝗼𝘀 𝗼𝗻 𝗻𝘂𝗺𝗯𝗲𝗿 𝘁𝗵𝗲𝗼𝗿𝘆.

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