Tags » Group Theory

No Eckmann-Hilton

Prove the following two statements and conclude that the fundamental group of a (connected) topological group is abelian:

1) A discrete normal subgroup of a connected topological group is central. 30 more words

Reading the Comics, December 30, 2017: Looking To 2018 Edition

The last full week of 2017 was also a slow one for mathematically-themed comic strips. You can tell by how many bits of marginally relevant stuff I include. 584 more words

Math

Fermat’s Little Theorem: proof by group theory

It’s time for our third and final proof of Fermat’s Little Theorem, this time using some group theory. This proof is probably the shortest—explaining this proof to a professional mathematician would probably take only a single sentence—but requires you to know some group theory as background. 390 more words

Number Theory

Rank isn't like dimension

Let be the free group in the generators and . Consider the group morphism defined by . Prove that is a free group of infinite rank. (Hint: Think topologically!)

Group Theory 101

Hello Readers,

This is a “back to basics” blog.  After all, not everyone has the high IQ necessary to enjoy Rick and Morty or my… 935 more words

How to get GAP4 to describe a group

This is a command that’s tough to Google even if you know it exists.  To get GAP to describe a group with a common, human-readable name, you can use the… 20 more words

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. 501 more words

Algebra