3 papers
math.GR2020
Classifying groups with a small number of subgroups
David A. Nash, Alexander Betz
We provide lower bounds on the number of subgroups of a group as a function of the primes and exponents appearing in the prime factorization of . Using these bounds, we cl…
math.GR2019
On the odd order composition factors of finite linear groups
Alexander Betz, Max Chao-Haft, Ting Gong +2
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 ab…
math.GR2019
Finite Permutation Groups with Few Orbits Under the Action on the Power Set
Alexander Betz, Max Chao-Haft, Ting Gong +3
We study the orbits under the natural action of a permutation group on the powerset . The permutation groups having exactly o…