Tags » Group Theory

short exact sequence and center

Let us prove:

Let be a short exact sequence, if the center  then

Proof:  When then , so .

Therefore

Algebra

New groups out of old (part 1)

Here’s my introduction to groups and the cyclic groups. The introduction to dihedral groups may also help.

We’ve seen the cyclic groups. These are exactly the groups that can be… 1,385 more words

Group Theory

Prees, prees, pretty prees

Last weekend I had a wonderful time at the Cornell Topology Festival- I went because my internet and now real life friend tweeted about it!   964 more words

Math

A distraction: infinite groups

This is the first in the distraction series. In these posts (put in the Group Theory-distractions category) I will explain something that I think is interesting and compliments the main material, but would be less likely to be seen in an early course on group theory. 1,188 more words

Group Theory

Introduction to random groups

Last summer, I participated in an awesome research program which ended up with a good handful of original research projects all having to do with  1,069 more words

Math

So I promised you symmetries...(part 2)

Here’s my introduction to groups and also part 1 of this topic.

Recall our example of the rotations of a square:

At the end of part 1, I asked where we’d seen the infinite cyclic group before. 1,733 more words

Group Theory

So I promised you symmetries...

Hello again and welcome! Following from my first post about group theory I figured I aught to give you a better overview by giving examples which will form a foundation for further study. 1,834 more words

Group Theory