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

## Tags » Group Theory

#### Conference announcement

The organisers have asked me to advertise this event, which I am happy to do The closing date for reduced rate registration is at the end of March. 209 more words

#### Group Theory

Group theory is the study of algebraic structures known as groups. It has many important applications in physics, chemistry and material science. It also has important applications in public key cryptography. 437 more words

#### A Generalization of Wilson's Theorem (due to Gauss)

John Wilson (1741-1793) was a well-known English mathematician in his time, whose legacy lives on in his eponymous result, *Wilson’s Theorem*. To recall, this is the statement that an integer is prime if and only if… 1,015 more words

#### Permutation Groups vis-à-vis Conformal Maps of the Riemann Sphere

In this post, we discuss a few ways in which the symmetric and alternating groups can be realized as finite collections of self-maps on the Riemann sphere. 1,820 more words

#### Formal Groups and Where to Find Them

In 1946, S. Bochner published the paper *Formal Lie Groups, *in which he noted that several classical theorems (due to Sophus Lie) concerning infinitesimal transformations… 1,823 more words

#### The Orders of Simple Groups

In 1832, Galois introduced the concept of normal subgroups, and proved that the groups (for ) and (for ) were ** simple**, i.e. admit no non-trivial (proper) normal subgroups. 1,364 more words