Tags » Group Theory

Hopf fibration double covers circle bundle of sphere

Two days ago, I gave a seminar talk on Chern‘s proof of the generalized Gauss-Bonnet theorem. Here I record the answer to a question asked by one of my colleague during the talk. 497 more words

Algebra

I Don't Understand Brackets

Ups and downs. It’s been such an eventful week. So much happened that made me rethink my time schedule.

Success

A few months ago, I’ve participated in Bundeswettbewerb Mathematik… 1,010 more words

TUM

Get the multiplication table of 2 by 2 matrices of integers modulo 3 - SageMath

The following code will prepare a list of two by two matrices over Z_2 and will show the group multiplication in it. Copy paste the code to a SageMath cell and try! 180 more words

Group Theory

A observation on conjugate subgroups

Let and be conjugate subgroups of , that is, for some , . Equivalently, , which means there is some element of such that under the action of on , its stabilizer subgroup is , all of the group of the group action. 68 more words

Algebra

Group of order p^2

I discussed this theorem with my grandfather when I went to Chennai this summer. I had learnt about group actions earlier, in the context of using group actions to solve combinatorial problems. 353 more words

Group Theory

Math sunday

I had a chill day thinking about math today without any pressure whatsoever. First I figured out, calculating inductively, that the order of is . You calculate the number of -tuples of column vectors linear independent and from there derive as the number of vectors that cannot be appended if linear independence is to be preserved. 693 more words

Algebra

Composition series

My friend after some time in industry is back in school, currently taking graduate algebra. I was today looking at one of his homework and in particular, I thought about and worked out one of the problems, which is to prove the uniqueness part of the Jordan-Hölder theorem. 138 more words

Algebra