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### Which one result in mathematics has surprised you the most? [closed]

A large part of my fascination in mathematics is because of some very surprising results that I have seen there. I remember one I found very hard to swallow when I first encountered it, was what is ...
34k views

### Examples of finite nonabelian groups.

Can anybody provide some examples of finite nonabelian groups which are not symmetric groups or dihedral groups?
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### Rubik's Cube Not a Group?

I read online that although the 3x3x3 is a great example of a mathematical group, larger cubes aren't groups at all. How can that be true? There is obviously an identity and it is closed, so that ...
905 views

### If $S$ is a nonempty subset of group $G$, then $S^{|G|}$ is a subgroup of $G$.

Let $G$ be a group with $|G| = n$ and let $\emptyset \ne S \subseteq G$. I want to show that $S^n$ is a subgroup of $G$ where by $S^n$ I mean the set $\lbrace s_1\cdots s_n \; | \; s_i \in S\rbrace$...
294 views

### Examples of sets which are not obviously sets

In my (limited) experience, it is usually easy to see when something is large enough to be a proper class, by constructing an element of the class for every set. However, sometimes such a proper ...
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### Nice examples of finite things which are not obviously finite

This question is in the spirit of the question "Nice examples of groups which are not obviously groups". There are many impressive finiteness results in mathematics. For example: The finiteness of \$\...
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### In what way is combinatorial game theory connected to the rest of mathematics?

Since my University library lists Conway's "Winning ways for your mathematical plays in the section "recreational mathematics" alongside books on origami and puzzles, I wondered to what extent game ...
253 views

### Soft question about irreducible representations

So I'm a beginner in representation theory and I'm a bit confused about the 'point' of irreducible representations. From what I understand, irreducible representations are important because they allow ...