5 problems

Durbin–McDonald’s converse conjecture. If $G$ has no direct factor isomorphic to $V$, then supersolvability of $\operatorname{Aut}(G)$ implies that $G$ is ultrasolvable.

Let $G$ be a finite non-solvable group. For a positive integer $n$, call $G$ an $S^{n}$-group if it has exactly $n$ non-nilpotent subgroups. Zarrin's conjecture. If $G$ is an…

T3arn3131ceanu's conjecture. If

Supersolvability conjecture. If

Consider a finite group $G$. Let $m$ denote the minimal dimension of a faithful completely reducible representation of $G$, let $\operatorname{MaxDim}$ denote the maximum size of a…