User:R-a-jones: Difference between revisions
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* [[Correspondence between normal subgroups and the kernels of characters of a finite group]] | * [[Correspondence between normal subgroups and the kernels of characters of a finite group]] | ||
* [[Number of real conjugacy classes is equal to number of irreducible real characters]] | * [[Number of real conjugacy classes is equal to number of irreducible real characters]] | ||
* [[Mackey’s restriction formula]] | |||
==Other contributions== | ==Other contributions== | ||
Revision as of 13:19, 8 November 2023
I'm a third year maths student in the UK.
I intend to fill out this wiki with groups related stuff I know from my degree.
Representation theory articles
I'm contributing to articles on representation theory as I learn it - in particular I am trying to add examples to example-less articles on definitions, or applications of results.
Contributions
Non-exhaustive list.
- Irreducible complex representation of abelian group is one dimensional
- Kernel of representation of finite group is set of elements where the character evaluates to dimension of representation
- Representation is irreducible if and only if inner product of character is 1
- Character of a linear representation - much of the content on this page.
- Sum of irreducible representation on conjugacy class is scalar multiple of identity matrix
- Linear representation theory of general affine group:GA(1,5)
- Sum of elements in row of character table of finite group is non-negative integer
- Correspondence between normal subgroups and the kernels of characters of a finite group
- Number of real conjugacy classes is equal to number of irreducible real characters
- Mackey’s restriction formula
Other contributions
Non-exhaustive list.
- Group of units modulo n
- Group of units modulo prime power is cyclic (statement. Proof to be filled in)
- The special case Group of units modulo prime is cyclic of the above. Statement and proof.
- Group of units modulo two times prime power is cyclic (statement. Proof to be filled in)
- Cyclic group:Z21 and the majority of the content on frobenius group of order 21
- Automorphism group of Zp for p prime is isomorphic to Z(p-1) (statement, proof to be filled in)
- Derived subgroup of dihedral group
- Derived subgroup is trivial if and only if group is abelian
- Class function (links and vector spaces bit)
- Vector space
- Automorphism group of cyclic group
- Generalized quaternion group:Q16's Cayley table
- Orbit under group action
- Homomorphic image of subgroup is subgroup
- Self-inverse conjugacy class
- Galois group of a polynomial
- Primitive element theorem
- Galois field extension
Groups of small orders
For my own persual if I need to look something up, but also may help you, pages for groups of small orders are in this table below. I intend to create more of these pages, where the order is sufficiently interesting (primes are not so interesting, neither are 2*primes, or primes^2, for example.)
General orders: pq, 2p, 4p (p is congruent to 1 mod 4, p is congruent to 3 mod 4), p^3, p^4, 2pq