this group is great,… if you don’t believe checkout:
there, it is its supergroup GL_2(Z_3).
the missing matrix in this photo is
Follow the links to get acquainted with the contents what we will work this semester.
Also, let me feedback you mentioning the topics which can be get into it to work on thesis (B.Sc. or M.Sc.) or else
- differential geometry
- differential topology
- low dimensional topology
- algebra and analysis
- sum of reciprocal inverses integers problem
These are fun really!
Filed under 3-manifolds, algebra, fiber bundle, geometry, latex, low dimensional topology, math, mathematics, multilinear algebra, sum of reciprocals, what is math
We are going to reconstruct the salient of a part of the classical theorem:
Each p-S of is contained into a p-SS of
Here the reference frame:
1. p-SS divides :
The set p-SS must be considered as an orbit of the action p-SS p-SS via . Since from sylow II we know that each two are conjugated the there is only one orbit
giving us a trivial orbital partition. Then p-SS=, i.e.
because for the isotropy group is .
2. Observe also that #p-SS:
since and , as far as
which implies that p-SS, then p-SS.
Proof of Theorem:
Considering the conjugation sub-action
we get a orbit decomposition p-SS = with the corresponding class equation
#p-SS = ,
but asumming that then
#p-SS = .
Now since #p-SS then there is some for which , so
With that, it is easy these: and is normal in .
Also given by is an epimorphism, so by the fundamental theorem of group-morphisms we have
Observing that and then
but is maximal, then . Hence and
Confer Milne Chapter 5