On the Davenport constant and group algebras

Details On the Davenport constant and group algebras On the Davenport constant and group algebras

2009-07-28

arxiv.org/abs/0907.4913v2

Colloq. Math. 121 (2010), 179-193

Mathematics

Combinatorics

12 pages; fixed typos and clearer proof of Lemma 3.9

Scientific paper

10.4064/cm121-2-2

For a finite abelian group $G$ and a splitting field $K$ of $G$, let $d(G, K)$ denote the largest integer $l \in \N$ for which there is a sequence $S = g_1 \cdot ... \cdot g_l$ over $G$ such that $(X^{g_1} - a_1) \cdot ... \cdot (X^{g_l} - a_l) \ne 0 \in K[G]$ for all $a_1, ..., a_l \in K^{\times}$. If $D(G)$ denotes the Davenport constant of $G$, then there is the straightforward inequality $D(G)-1 \le d (G, K)$. Equality holds for a variety of groups, and a standing conjecture of W. Gao et.al. states that equality holds for all groups. We offer further groups for which equality holds, but we also give the first examples of groups $G$ for which $D(G) -1 < d(G, K)$ holds. Thus we disprove the conjecture.

Affiliated with

Also associated with

No associations

Rating

On the Davenport constant and group algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Davenport constant and group algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Davenport constant and group algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-682167