No simple groups of order 66 or 144.

We look at an "advanced" group theory problem that uses Sylow's Theorems to show that there are no simple groups of order 66 or 144. Suggest a problem: https://forms.gle/ea7Pw7HcKePGB4my5 Please Subscribe: https://www.youtube.com/michaelpennma... Merch: https://teespring.com/stores/michael-... Personal Website: http://www.michael-penn.net Randolph College Math: http://www.randolphcollege.edu/mathem... Randolph College Math and Science on Facebook:   / randolph.science   Research Gate profile: https://www.researchgate.net/profile/... Google Scholar profile: https://scholar.google.com/citations?... If you are going to use an ad-blocker, considering using brave and tipping me BAT! https://brave.com/sdp793 Buy textbooks here and help me out: https://amzn.to/31Bj9ye Buy an amazon gift card and help me out: https://amzn.to/2PComAf Books I like: Sacred Mathematics: Japanese Temple Geometry: https://amzn.to/2ZIadH9 Electricity and Magnetism for Mathematicians: https://amzn.to/2H8ePzL Abstract Algebra: Judson(online): http://abstract.ups.edu/ Judson(print): https://amzn.to/2Xg92wD Dummit and Foote: https://amzn.to/2zYOrok Gallian: https://amzn.to/2zg4YEo Artin: https://amzn.to/2LQ8l7C Differential Forms: Bachman: https://amzn.to/2z9wljH Number Theory: Crisman(online): http://math.gordon.edu/ntic/ Strayer: https://amzn.to/3bXwLah Andrews: https://amzn.to/2zWlOZ0 Analysis: Abbot: https://amzn.to/3cwYtuF How to think about Analysis: https://amzn.to/2AIhwVm Calculus: OpenStax(online): https://openstax.org/subjects/math OpenStax Vol 1: https://amzn.to/2zlreN8 OpenStax Vol 2: https://amzn.to/2TtwoxH OpenStax Vol 3: https://amzn.to/3bPJ3Bn My Filming Equipment: Camera: https://amzn.to/3kx2JzE Lense: https://amzn.to/2PFxPXA Audio Recorder: https://amzn.to/2XLzkaZ Microphones: https://amzn.to/3fJED0T Lights: https://amzn.to/2XHxRT0 White Chalk: https://amzn.to/3ipu3Oh Color Chalk: https://amzn.to/2XL6eIJ