User:R-a-jones: Difference between revisions
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** The special case [[Group of units modulo prime is cyclic]] of the above. Statement and proof. | ** 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) | * [[Group of units modulo two times prime power is cyclic]] (statement. Proof to be filled in) | ||
* [[Automorphism group of Zp for p prime is isomorphic to Z(p-1)]] (statement, proof to be filled in) | * [[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 of dihedral group]] | ||
Revision as of 22:33, 27 December 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.
Handy wiki-editing pages
Special:SpecialPages Special:WantedPages
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.
- Completely reducible linear representation
- Representation of finite group over field of characteristic zero decomposes as direct sum of irreducible subrepresentations
- 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
- Decomposable group
- Symmetric and alternating-squares of linear representation
- Linear representation theory of circle group
- Irreducible representation of dimension greater than one will have character equal to zero on some conjugacy class
- Group of odd order has only one real-valued irreducible character
Mackey theory
Other contributions
See also: Special:Contributions/R-a-jones
Non-exhaustive list.
- List of groups of order 64
- 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)
- 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 with same character table need not be isomorphic
- Gnu function and moa function
- Abelian number
- Finite group of odd order has no non-trivial elements conjugate to their inverse Statement. Proof to be filled in.
- Modular maximal-cyclic group
- Transitive subgroup of symmetric group
- Number of groups of order n up to isomorphism is at most n to the power of (n log base 2 n)
- Non-isomorphic simple groups may have the same order
- Prüfer group
- Leinster group
Groups of small orders
See User:R-a-jones/Groups of small orders for a long list of pages on groups of a particular order.