21.68 (2026)

A finite group $G$ is said to be semi-abelian if it has a sequence of subgroups $1 = G_0 \leqslant G_1 \leqslant \dots \leqslant G_n = G$ such that for every $i$ the subgroup $G_{i+1}$ is isomorphic to a quotient of a semidirect product $A_i \rtimes G_i$ for some abelian group $A_i$.

Conjecture: Semi-abelian finite groups are monomial.