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

## Tags » Group Theory

#### 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

#### 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