All Questions

Let $G$ be a subgroup of the permutation group $S_n$, and let $H$ be a normal subgroup of $G$ such that the quotient group $G/H$ is abelian. What is the best known upper estimate for the cardinality $...

Let us consider $\mathbb{Z}_N=\{0,1,\cdots N-1\}$. Does there exist any permutation $\sigma$ on $\mathbb{Z}_N$ satisfying : $$\exists p,q\in\mathbb{N}, ~~p,q\neq0 (mod~N) ~~\forall i,j\in \mathbb{Z}...

A number $n$ is called insipid if the groups having a core-free maximal subgroup of index $n$ are exactly $A_n$ and $S_n$. There is an OEIS enter for these numbers: A102842. There are exactly $486$ ...