Cauchy's Theorem in group theory

[@SreenathSreekrishna]

Wow! This is kind of like a generalization of Fermat's little theorem, but for any group. Thanks for sharing this with us!

[@minamagdy4126]

FLT is more of a for-all statement while here we have an existence statement. They do feel linked in some way, though...

[@Noam_.Menashe]

Fermat's little theorem is just Lagrange's theorem (order of subgroup must divide order of group) on a multiplicative group {1,2,..p-1} where p is prime and we take things modulo p. Specifically using the sub-group generated by powers of any element.

[@Adraria8]

Really cool theorem, REALLY cool proof!

[@brandonwillnecker8060]

6:49 mp being Michael Penn?😂

[@joseluishablutzelaceijas928]

Interesting is also noting that the claim at 17:17 implies that the number of distinct elements of order p is a multiple of p.

[@goodplacetostop2973]

18:48

[@natepolidoro4565]

Augustin-Louis Cauchy was a legend

[@kumaraditya829]

Thanks a lot Michael….Abstract Algebra could not have been explained in any better and crude way than this!

[@naffouri]

This is technically proving a stronger statement: that there is at least p-1 elements of order p

[@addafarouk839]

A very constructive and beautiful proof.❤

[@joshuagiir]

we love mp!!!

[@seedmole]

Nice, the theorem basically describes a bunch of what I've picked up about modulo mathematics through stuff like experimental music making techniques.

[@armanavagyan1876]

Thanks for sharing every day a new video ☺

[@azur6830]

Exactly what i needed 😂

[@Alan-zf2tt]

Sometimes i think that precise definitions take away some of the beauty that happens in math. And then I ponder that sequences of guided operations can be defined in a very precise way and doing so has a beauty of its own.

[@richardchapman1592]

Was short of the what D(n)gon is a generalisation of so missed the connection to prime factors.

[@addafarouk839]

We can therefore conclude, as a corollary, that every group of prime order is cyclic.

[@shoryaprakash8945]

I remember this proof this is quite an elegant way to prove it. There is an another way to prove this i.e. by induction.

[@martinb3000]

11:55 I don't get it. In the illustrative p=3 case, why use elements from the equivalence classes for p=4? Shouldn't it be g1 g2 g3, g2 g3 g1, g3 g1 g2, and "multiples" of those?

[@fluffiness100]

The last entry is the product of g2 inverse and g1 inverse, so there are only 3 entries in total. As stated beforehand, the last entry is determined entirely by the previous entries.

[@tornation5609]

Correction: this theorem is just a consequence of Lagrange's Theorem

[@eartphoze]

in my own written words, I believe explaing is more important than interpreting. identity of a group, as the last mark of chalk suggest, the moon is made of chalk. Explained through terms inside parenthesis given text over video, speed over time and space. Poetry interpreted not compiled time, only run time. boolean = false.