User:R-a-jones

I have a bachelor's degree in mathematics.

I intend to fill out this wiki with groups related stuff I know from my degree.

Handy wiki-editing pages

Special:SpecialPages Special:WantedPages

Pages to be deleted

I cannot delete pages, but the pages at the following category should probably be deleted. Will flag with admin when there are a significant number of pages in this category.

Category:Flagged by User:R-a-jones to be deleted

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.
  • Irreducible character of a linear representation
• 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

• Mackey’s restriction formula

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.

Also see User:R-a-jones/Groups of order list prime factors