Tags » Group Theory

Isomorphic groups from linear algebra

Although algebraic structures (such that groups, rings, fields, etc.) are generally difficult to classify, surprisingly linear algebra tells us that vector spaces (over a fixed field) are classified up to isomorphism by only one number: the dimension! 299 more words

Abelian Groups

a poem, a strategic lemma

Lemma

 

,

such that .

Proof:

By employing the Double Coset Counting Formula we have , and since  then  such that .

But so , hence, having , this implies that , where .

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Math

How violent protests start: Learning from the Buffalo

Here we will examine the common processes that lead to violent processes across contexts and situations. Notice how it takes only one leader and a few followers, to get the many buffalo to attack the lions that are eating their friend. 334 more words
Psychology

On the joy of getting something right

Last week I had a particularly bad day at work.  I went to a meeting where just about every behaviour I warn students about was on display.   533 more words

Textiles

A Course in Mathematics

In recent months, I’ve taken a strong interest in Mathematics. Much stronger than what I had in Secondary and Third Level Education. It started with Cryptography and Encryption, but I soon learned I may be out of my depths if I don’t take a step back and brush up on other areas first. 266 more words

Security

Representation theory of finite groups and commutativity degree

If is a finite group, we define its commutativity degree as the probability that two elements of commute, that is

It is surprising that the value of may give strong information about . 1,375 more words

Probability