On totally k-closed nilpotent groups

2023/12/24 by Д. В. Чуриков, Churikov, Dmitry
Computer Science · Engineering · Mathematics · #05E18 #20B25 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2312.15456

openalex publication_date 2023/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A group G is said to be totally k-closed for a positive integer k if, in each of its faithful permutation representations on a set Ω^k, G is the largest subgroup of the symmetric group Sym(Ω) that preserves every k-orbit in the induced action on the set Ω×…× Ω=Ω^k. We prove that for k≥1, every finite nilpotent group with Sylow subgroups of orders at most p^k for all primes p dividing |G| is totally k-closed if and only if it does not contain an elementary abelian subgroup ℤ_p^k for every prime p.

Related

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• On finite totally k-closed groups
• Structure of k-closures of finite nilpotent permutation groups
• On finite totally 2-closed groups
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