Two-closure of supersolvable permutation group in polynomial time

Abstract

The $2$-closure $\overline{G}$ of a permutation group $G$ on $\Omega$ is defined to be the largest permutation group on $\Omega$, having the same orbits on $\Omega \times \Omega$ as $G$. It is proved that if $G$ is supersolvable, then $\overline{G}$ can be found in polynomial time in $|\Omega |$. As a byproduct of our technique, it is shown that the composition factors of $\overline{G}$ are cyclic or alternating of prime degree.

20 pages

Cited by in corpus (3)

• The $3$-closure of a solvable permutation group is solvable
• On computing the closures of solvable permutation groups
• Closures of permutation groups with restricted nonabelian composition factors