Monthly Archives: May 2017

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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