Search Results

$SU(n)$ acts freely on $\Bbb C^n\setminus 0$ (not on $\Bbb C^n$) for $n=1,2$, but not for higher $n$ (the stabilizer of a point is $SU(n-1)$). If this is what you are asking about, the answer is "yes" …

Let $U_n$ be the group of upper triangular integer matrices of size $n$ by $n$ with ones on the diagonal. Then $U_n$ is generated by the elements $x_i$, $i=1,...,n-1$, with Serre relations $$ [x_i,[x …

This summer I developed a minicourse for high school students in group theory. We discussed the game of 15, SET, wallpaper patterns, and Rubik's cube. Maybe this could be helpful: www-math.mit.edu/ …

One of the simplest consequences of Sylow's first theorem is the Cauchy theorem, saying that a group of order divisible by a prime $p$ contains an element of order $p$. I'd like to point out that th …

Here is a short proof of the weaker version of the statement from Question 1 (giving a polynomial with rational coefficients). Let's think of characters as functions on conjugacy classes. Then $\chi(1 …