Year: 2024
Type: preprint
Abstract: Let $G$ be a group and $A\subseteq [1,\exp(G)-1]$. We define the constant ${\sf C}_A(G),$ which is the least positive integer $\ell$ such that every sequence over $G$ of length at least $\ell$ has an $A$-weighted consecutive product-one subsequence. In this paper, among other things, we prove that ${\sf C}_A(C_n^2)=4$ with $A=[1,n-1],$ and ${\sf C}(H\times K)=|H||K|$, where $H$ is a finite abelian group and $K$ is a metacyclic group.
Source: arXiv (Cornell University)
Authors: Lemos, A., Moura, A. O., Ribas, S., Silva, A. T.
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394947645