Let $G = G_{1} \times G_{2}$. I need to prove the following two things: If $G_{i}$ is nilpotent of degree $n_{i}$, $i = 1, 2$, then $G$ is nilpotent of degree $n = \max \{ n_{1}, n_{2} \}$. If $G_{i}$ is solvable (some people call them soluble) of degree $n_{i}$, $i = 1,2$, then $G$ is solvabl...

This is an old question, but it's still interesting. Here is a more precise version of it: Definition. Let $f\colon\mathbb{C}\to\widehat{\mathbb{C}}$ be a meromorphic function. A Euclidean isometry $g\colon \mathbb{C}\to\mathbb{C}$ is a symmetry of $G$ if $f(g(z))=f(z)$ for all $z\in\mathbb{C...

This is more of a theoretical question, but I'm having trouble understanding why it is that Latin squares are generalizations of a group? I kind of arrived at this question trying to figure out why independent vectors were so important in linear algebra. To phrase the question differently, wh...