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group theory - A kind of converse of Lagrange's Theorem - Mathematics Stack Exchange
In addition to Cauchy's Theorem and Sylow's Theorems, there is also Hall's Theorem, which states that if G is solvable, |G|=mn with gcd(m,n)=1, then G has a subgroup of order m, and conversely, that if G has this property, then G is solvable.
math.GR 
october 2018 by quamash
The Easiest Way to Memorize the Algorithms of Rubik's Cube: 7 Steps
Learn to solve the Rubik’s cube in no time by taking advantage of your visual memory. You’ve probably been playing with Rubik’s cube and wondering how to solve it. Eventually, you may have succeeded by following an online tutorial. While there are several methods to solve the 3x3 cube, these techniques usually consist of a number of algorithms that look something like this: T R Ti Ri Ti Fi T F.

Some people can memorize such sequences without difficulty. But what about the rest of us who are better at remembering peoples faces rather than their names? The good news is that the algorithms can be converted into easy to memorize graphics so that you don’t need to spend days learning the sequences by heart!
diy  puzzles  visuo  spatial  explanation  howto  math.GR  rec-math  wordlessness 
july 2017 by nhaliday
5/8 bound in group theory - MathOverflow
very elegant proof (remember sum d_i^2 = |G| and # irreducible rep.s = # conjugacy classes)
q-n-a  overflow  math  tidbits  proofs  math.RT  math.GR  oly  commutativity  pigeonhole-markov  nibble  shift 
january 2017 by nhaliday

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