Questions tagged [solvable-groups]

Does every finite group $G$ have a factorization $G=H_1\cdots H_k$ where the $H_i$ for $1\le i\le k$ are solvable subgroups of $G$ and $|G|=|H_1|\cdots |H_k|$ (equivalently, every element of $G$ is ...

I have two questions about the class of integer-coefficient polynomials all of whose roots are rational. I asked this at MSE, but it attracted little interest (perhaps because it is not interesting!) ...

Is it possible to give a reasonable description of those finite solvable groups $G$ such that $A = {\rm Aut}(G)$ is also solvable? The central case to deal with is that in which $G$ is a $p$-group of ...