Ziv’s Math World

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Abstract Algebra – Sylow Theorems and Its applications

In abstract algebra, finite group theory is in its core. Now from Lagrange theorem, we have Lemma 1 Let be a subgroup of a finite group . Then the order of is a divisor of the order of . This theorem states the necessary condition for a finite group to be a subgroup of a…

December 2024
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  • Abstract Algebra – Sylow Theorems and Its applications

    In abstract algebra, finite group theory is in its core. Now from Lagrange theorem, we have Lemma 1 Let be a subgroup of a finite group . Then the order of is a divisor of the order of . This theorem states the necessary condition for a finite group to be a subgroup of a […]

    ../..

  • An approximation problem

    Problem: Let us call an irrational number well approximated by rational numbers if for any natural numbers there exists a rational number such that     Solution: 1. Pick     Why does it work ? Let’s say we let . Then we have     and     We now proceed in proving that […]

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  • The Fastest Web Hosting Service Provider Fozzy com

    Rent Game Server Hosting at Fozzy Feel the Joy of Playing Together Just keep in mind that it has 10+ years of experience under its belt and has all the features for an awesome online gaming experience. You can foun additiona information about ai customer service and artificial intelligence and NLP. We use dedicated people […]

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  • On IMO2017 P2

    I did IMO 2017 P2 with my friends yesterday. Now I would like to share my thoughts on this problem. Problem: Let be the set of real numbers. Determine all functions such that, for any real numbers and ,     The initial step must be taking certain values, testing its properties and then start […]

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