On finite totally k-closed groups

2024/02/27 by He, Jiawei, Li, Xiaogang
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2402.17240

Abstract

Let G be a finite group acting faithfully on a finite set Ω. For a positive integer k, G acts naturally on the Catesian product Ω^k := Ω× ...× Ω. In this paper, we prove that finite nilpotent group G with 2\nmid |G| is a totally k-closed group if and only if G is abelian with n(G)≤ k-1 or cyclic, where n(G) is the number of invariant factors in the invariant factor decomposition of G.

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