Category Archives: Group Theory

“One Line” Algebra Qual Problems

Today I’m going to try to distill some solutions to previous algebra qual problems into one sentence answers. This will likely mean that the solutions are missing details, but my hope is to be able to give a decent overview … Continue reading

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Groups of order 4,312 are not simple: An application of Sylow Theory

Today we will solve a problem from Wisconsin’s 2012 Algebra Qualifying Exam. The main tools used in the problem are Sylow Theory and group actions; we will take these tools for granted, but for great introductions to each topic I would … Continue reading

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Cauchy’s Theorem

The famous Lagrange’s Theorem states that, in any finite group , the order of any element divides the order of . A natural follow up to this theorem is whether or not the converse holds. That is, if divides the order of … Continue reading

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