## Tags » Group Theory

#### Basic Concept of a Group

A fundamental part of Group Theory is the definition of a Group.

A Group (G) is:

- a set of mathematical objects, either infinite in size, or finite in size … 149 more words

#### Proof That Every Finite Integral Domain is a Field

Here is a proof that I’ve always found to be very elegant. Recall that an integral domain is defined as a commutative ring with unity and no zero divisors. 247 more words

#### Sylow subgroups of symmetric groups

The purpose of this post is to collect some proof of known results on Sylow subgroups of symmetric groups that are scattered across the literature, and in one case, wrongly stated in the standard reference. 1,800 more words

#### The End 2016 Mathematics A To Z: Kernel

I told you that Image thing would reappear. Meanwhile I learned something about myself in writing this.

## Kernel.

I want to talk about functions again. I’ve been keeping like a proper mathematician to a nice general idea of what a function is. 1,189 more words

#### An Interesting Problem Involving Subgroups

I was given a problem last week which involved proving whether or not a specified algebraic system proposed was supposedly a subgroup of a group. Let us attempt a formal proof for the problem. 155 more words

#### Lisbon 2016

As the picture (medronho fruit and eucalyptus leaves) might suggest, I am in Portugal: this was taken in Monsanto (not the wicked chemical company but the forest park on a hill just west of Lisbon). 50 more words