Tags » Group Theory

Burnside's method

Burnside proved in 1901 that if is an odd prime then a permutation group containing a regular subgroup isomorphic to is either imprimitive or 2-transitive. His proof was an early applications of character theory to permutation groups. 423 more words

Linear Algebra

Are There More Sets or Groups?

In an effort to procrastinate from revising for my exams next month, I pondered the question of whether or not there are more sets than groups. 360 more words


Taking on the Rubik's Cube

Group theory is so often seen as a highly abstract area of Mathematics and it seems difficult to imagine how it could be applied in the real world. 130 more words


Rotations in Three Dimensions

In Rotating and Reflecting Vectors Using Matrices we learned how to express rotations in -dimensional space using certain special matrices which form a group (see… 1,206 more words


Spooky algebra II

Exhibit a group , a set of generators for and a subgroup such that for all and yet is not normal in .

Group Therapy

The study of groups cleanses the soul. This post will define the concept of a group and show a few simple results, after this there will be several different directions to go in for future posts. 438 more words


Regular abelian subgroups of permutation groups

A B-group is a group such that if is a permutation group containing as a regular subgroup then is either imprimitive or -transitive. (Regular subgroups are always transitive in this post.) The term ‘B-group’ was introduced by Wielandt, in honour of Burnside, who showed in 1901 that if is an odd prime then is a B-group. 1,440 more words

Symmetric Group