All Questions

Let $G$ be a finite solvable group which is not nilpotent, and let $H=[G,G]$ be the commutator subgroup of $G$. Does the following hold for $G$ and $H$? "There exists $g \in G \setminus H$ and $h ...

Denote the commuting probability (the probability that two randomly chosen elements commute) of a finite group $G$ by $\operatorname{cp}(G)$. By a result of Gustafson [2], $\operatorname{cp}(G)=\...