English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $G$ be a finite group, written multiplicatively. The Davenport constantof $G$ is the smallest positive integer $D(G)$ such that every sequence of $G$with $D(G)$ elements has a non-empty subsequence with product $1$. Let $D_{2n}$be the Dihedral Group of order $2n$ and $Q_{4n}$ be the Dicyclic Group of order$4n$. J. J. Zhuang and W. Gao (European J. Combin. 26 (2005), 1053-1059) showedthat $D(D_{2n}) = n+1$ and J. Bass (J. Number Theory 126 (2007), 217-236)showed that $D(Q_{4n}) = 2n+1$. In this paper, we give explicitcharacterizations of all sequences $S$ of $G$ such that $|S| = D(G) - 1$ and$S$ is free of subsequences whose product is $1$, where $G$ is equal to$D_{2n}$ or $Q_{4n}$ for some $n$.

Extremal product-one free sequences in Dihedral and Dicyclic groups