As of May 4 2007 the scripts will autodetect your timezone settings. Nothing here has to be changed, but there are a few things

## Sunday, December 20, 2009

### Lecture 21 of Abstract Algebra E-222

Again the Sylow theorems and a summary of the proofs.
Then finite groups of certain orders were classified.
Order p, p prime. Cyclic groups of order p.
Order p * q, p > 2, p < q. Cyclic of order p*q and if p / (q-1): Cq : Cp.
Order 2p, cyclic of order 2p and the Dihedral groups Dp.
Order p^2*q. Started with order 12:
- C12
- C6 X C2
- A4
- D6
- C4 : C3.
- A4 = ( C2 X C2 ) : C3.

Gross sofar never talked about GAP, Mathematica, Magma or Maple. Group theory can get very complicated without the aid of a mathematics package. The groups were classified solely on the basis of the Sylow theorems in this lecture. The semi-direct product has not been lectured yet. For those new I would say these lectures were real hard. Unnecessarily hard in my opinion. The next lecture is about the Symmetry group by a famous number theory guy ( forgot his name ).

Anyway, I discovered an interesting fact about S6 today, the symmetry group on 6 letters. It is the only symmetric group whose automorphism group is not eqaul to the group itself. - Now, why would that be? Seems like some deep fact to me. - This is were mathematics gets a grip on you. You must know why.

## Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before

(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)