A polynomial bound for the number of maximal systems of imprimitivity of\n a finite transitive permutation group

2019/07/19 by Andrea Lucchini, Lucchini, Andrea, Mariapia Moscatiello +3 · 1 citation
Computer Science · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1907.08477

openalex publication_date 2019/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that, there exists a constant a such that, for every subgroup H\nof a finite group G, the number of maximal subgroups of G containing H is\nbounded above by a|G:H|^3/2. In particular, a transitive permutation group\nof degree n has at most an^3/2 maximal systems of imprimitivity. When G\nis soluble, generalizing a classic result of Tim Wall, we prove a much stroger\nbound, that is, the number of maximal subgroups of G containing H is at\nmost |G:H|-1.\n

Cited by

• Counting subgroups of a finite group containing a prescribed subgroup

Related

• Finding Blocks of Imprimitivity When There is a Small-Base Action on Blocks
• On the number of cyclic transitive subgroups of a permutation group
• Bounds for Finite Semiprimitive Permutation Groups: Order, Base Size,\n and Minimal Degree
• Imprimitive Permutations in Primitive Groups
• Maximal subgroups of finite soluble groups in general position