A conjecture on partitions of groups

2014/08/26 by Ігор Протасов, Protasov, Igor, Sergii Slobodianiuk +1
Computer Science · Mathematics · #03E05 #20B07 #20F69 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1408.6259

openalex publication_date 2014/08/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We conjecture that every infinite group G can be partitioned into countably many cells G=\bigcup_n∈ωA_n such that cov(A_nA_n^-1)=|G| for each n∈ω. Here cov(A)=min\|X|:X⊆ G, G=XA\. We confirm this conjecture for each group of regular cardinality and for some groups (in particular, Abelian) of an arbitrary cardinality.

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