Ken’s Group Theory Library

(Electronic articles)

Good elementary papers for MTH 523/MTH 623

Burns, The foundation period in the history of group theory, Monthly 1913.

Some history, in an article almost a century old!

Hayes, Group Theory in the bedroom.

An elementary introduction to groups via mattress flipping.

Kleiner, Evolution of Group Theory, a survey.

A valuable paper on the history of group theory.

MacHale, Minimum counterexamples in group theory.

A great paper on a variety of false statements and the smallest group providing a counterexample. (Very good for a course like MTH 623, Intro to groups, where, using GAP, one should be able to find some of the minimal counterexamples.

Wild, The groups of order 16 made easy, Math Monthly, Jan 2005, 20-31.

A great paper on the groups of order 16.

More sophisticated papers (for MTH 623)

Cameron, A short bibliography on classical groups or on my laptop.

Peter Cameron lists 24 references on classical groups.

Kisil, Starting with SL2R, or ArXiv 0607387

An introduction to questions arising from 2x2 matrices. Associations with linear fractional transformations.

J. S. Milne’s group theory notes

Minassian, A simple structure theorem for two-generator, one-relation groups, Monthly 1985.

Good application of semi-direct products, describing metacylic groups with a single relation.

Shapiro, Finite groups acting on sets with applications, Math Magazine, 1973.

An introduction to group actions.

Sharipov, Representations of Finite Groups, or ArXiv 0612104.

An online textbook on group representations.

Rather sophisticated (Some research papers, more difficult)

Adan-Bante, Induction of characters and finite p-groups. From the arXiv 0507355.

On induced characters of finite p-groups.

Banica, Bichon, On Quantum Automorphism Groups of Vertex-transitive Graphs of order le 11 or ArXiv 0601758.

Introduces quantum groups.

Bovdi, Hoffert, Kimmerle, The first Zassenhaus conjecture for integral group rings, or ArXiv 0507246.

Are the torsion units of an integral group ring conjugate to a group element?

Bovdi, Symmetric Units and group identities in group algebras, I or ArXiv 0607277.

Fulman, Convergence rates of random walks on irreducible representations of finite groups or ArXiv 0607399.

Helleloid, A survey on automorphism groups of finite p-groups, or ArXiv 0610294.

Hillar, Rhea, Automorphisms of Finite Abelian groups, or ArXiv 0605185.

James, Cannon, computations of isomorphism classes of finite p-groups, Math of Comp. 1969.

How to use isoclinism. This idea was eventually used in GAP.

Kambitos, Silva, Steinberg, Spectra of Lamplighter Groups and Cayley Machines or ArXiv 0412412.

On random walks on wreath products....

Konovalov, On the isomorphism problem of unit groups of modular group algebras or ArXiv 0607287.

Classifying 2-groups of order 32 or less by the “normalized unit group of their modular group algebra over the field of two elements.” Uses GAP and LAGUNA.

Mulvey and Resende, A noncommutative theory of Penrose tilings, or ArXiv 0306361.

Rattagi, Infinite groups generated by two quaternions, or ArXiv 0502512.

On infinite subgroups of the multiplicative group of the quaternions.

Savchev, Chen, Long n-zero free sequences in finite cyclic groups, or ArXiv 0604356.

Shanks and Wehlau, Decomposing Symmetric Powers of Certain Moduluar representations, or ArXiv 0509044.

It's about modular representations....

Steinberg, Moebius functions and representations of semigroups or ArXiv 0607564.

Characters of groups are generalized to semigroups using Mobius inversion.

Tsilevich & Vershik, Induced Representations of the Infinite Symmetric Group, or ArXiv 0605166.

Last updated December 26, 2006.