I have read many books about famous mathematicians, such as Pythagoras or Gauss, who lived many years ago, however I know little about modern mathematicians. So, I had the idea to start a series where I talk about those at the forefront of today’s research. 595 more words

## Tags » Group Theory

#### Online Math Tuition, Math tutors Saudi Arabia

## Online Math Tuition, Math tutors Saudi Arabia

Online Math Tuition, Math tutors Saudi Arabia Math teachers, B. Sc. Math tuition Saudi Arabia, online Math tuition, online Math tutors. 378 more words

#### [Research] Presentations of monoids and groups, basic positive reachability

This follows from this question on Math.StackExchange:

http://math.stackexchange.com/questions/1359035/presentation-of-groups-and-positive-expressions

The problem I described in this question is a problem of “basic positive reachability”. If a positive expression… 87 more words

#### [Research] There is always new parts of math to learn

I used to think that I have “learned” group theory. Later I know how wrong I was. I did learn a part of it in undergraduate school and reviewed it in my first year graduate Algebra class, but I always have new things to learn about group theory, such as tricks on group presentations, which I did not learn enough in class. 40 more words

#### Proof that any subgroup of index 2 is normal

Let be a subgroup of index 2.

Let and .

If , then , and , hence left coset equals to right coset.

If , then (set minus), and also , thus left coset also equals to right coset. 31 more words

#### Aut(Z_n): Automorphism Group of Z_n

Do check out our list of Recommended Undergraduate Math Books!

We prove that , also known as (easier to type).

Define by .

First we show that it is a homomorphism: 117 more words

#### Working with Cayley tables

The aim of this post is to familiarise you well enough with Cayley tables so that in the next post we can really pin down what it means for two groups to be the ‘same’. 1,031 more words