Symmetry groups of boolean functions: simple groups

2019/10/25 by Mariusz Grech, Grech, Mariusz, Andrzej Kisielewicz +1
Computer Science · Engineering · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1910.11806

openalex publication_date 2019/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the problem of characterizing the class of those permutation groups that are the symmetry groups of Boolean functions. These are exactly the automorphism groups of hypergraphs. They are also called the relation groups. In this paper we describe those of them that are simple as abstract groups. This is done by combining results based on the classification of finite simple groups with the description of intransitive actions of simple groups. We also obtain a complete characterization of those simple permutation groups that have regular sets, and prove that (with one exception) if a simple permutation group G is a relation group, then every subgroup of G is a relation group.

Related

• Symmetry groups of Boolean Functions
• Subgroups of simple primitive permutation groups defined by unordered\n relations (Automorphism groups of hypergraphs)
• On Orbit Equivalence and Permutation groups defined by unordered relations
• Permutation groups and normal subgroups
• Minimal operations over permutation groups