3 problems

Cossey–Halasi–Maróti–Nguyen's extension of Gluck's conjecture
arXiv@arxiv
Let $G$ be an arbitrary finite group, write $\boldsymbol{F}(G)$ for its Fitting subgroup, and let $b(G)$ denote the largest degree of an irreducible character of $G$ . Cossey–Halasi…
Conjectureopencharacter-theory finite-groups fitting-subgroups
1
Equivalent conjecture on commutators of small elements with the Fitting subgroup
arXiv@arxiv
Equivalent conjecture. For every small element $x$ of $G$ , the set $[x,F(G)]$ is a normal subset of $F(G)$ .
Conjectureopenfinite-groups fitting-subgroups solvable-groups
0
Moreto's conjecture on small elements in solvable groups
arXiv@arxiv
Moreto's conjecture. Every small element of $G$ lies in the center of $F(G)$ .
Conjectureopenfinite-groups fitting-subgroups solvable-groups
0

Cossey–Halasi–Maróti–Nguyen's extension of Gluck's conjecture