Anthony Ter-Saakov | Searcharxiv

arXiv2021

Finite Permutation Groups with Few Orbits Under the Action on the Power Set

We study the orbits under the natural action of a permutation group $G \subseteq S_n$ on the powerset $\mathscr{P}(\{1, \dots , n\})$. The permutation groups having exactly $n+1$ orbits on the powerset can be characterized as set-transitive groups and were fully classified in \cite{BP55}. In this paper, we establish a general method that allows one to classify the permutation groups with $n+r$ set-orbits for a given $r$, and apply it to integers $2 \leq r \leq 15$ using the computer algebra system GAP.

math.GR↗

arXiv2020

On the odd order composition factors of finite linear groups

In this paper, we study the product of orders of composition factors of odd order in a composition series of a finite linear group. First we generalize a result by Manz and Wolf about the order of solvable linear groups of odd order. Then we use this result to find bounds for the product of orders of composition factors of odd order in a composition series of a finite linear group.

math.GR↗