Category Archives: fiber bundle
the double coset counting formula is a relation inter double cosets , where and subgroups in . This is:
One is to be bounded to the study of the natural map . And it uses the second abstraction lemma.
The formula allows you to see the kinds of subgroups of arbitrary versus a of , for the set of the – Sylow subgroups.
Or, you can see that through the action via you can get:
- which comply the equi-partition
- , so , for some
then you can deduce:
Now, let us use those ideas to prove the next statement:
Let be a finite group, with cardinal , where each are primes with and positive integers.
Let be a subgroup of of index .
Then, is normal.
By employing in the double coset partition, one get the decomposition:
So by the double coset counting formula you arrive to:
From this, we get .
But as well so
Then . So for each .
This implies and so for all the posible , hence, is normal.
since we are requiring “canonical” duality, i.e. covectors, , do
that is, a curve ,…
what is math? let us discuss:
|Baby Abstract Multilinear Algebra|
|Baby Multilinear Algebra of Inner Product Spaces|
|Algebraic Differential Geometry||
|Baby Manifolds (topological, differential, analytic, anti-analytic, aritmetic,…)
||Examples: Lie groups and Fiber bundles|
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!