## Tags » Group Theory

Group Theory

Group Theory

#### Cosets, Abelian groups and Pauli matrices

The Group.rb class is updated with functions to calculate subgroup cosets and check commutativity. The attached test set uses Pauli matrices as an example of a non-commutative/non-Abelian group. 1,259 more words

# Mathematical Pearls

Collecting .

## Sum of squares

2014-03-04

two-square sum

$z = a + bi, \bar{z} = a – bi, |z| = \sqrt{a^2 + b^2}, z \bar{z} = a^2 + b^2$

397 more words
Group Theory

#### Groups with Ruby

I’ve started writing some functions for verifying introductory group theory results in order to gain a better understanding of group theory. So far, my Group class is able to determine whether a particular discrete set and operator combination is a group. 506 more words

#### AGRA II

I am now able to make this public: the second AGRA school (Aritmética, Grupos, Análisis) will be happening in Cusco in August 2015. 208 more words

#### Proof that the multiplicative group of a finite field is cyclic

Outline of the proof:

• Lemma: show that for any two elements and  with orders and  there is an element of the order ;
• Guess the generator (hint: it should have the largest order);
• 529 more words
Math