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

## Tags » Group Theory

#### 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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#### 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

#### 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

#### 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