Generating abelian groups by addition only

Details Generating abelian groups by addition only Generating abelian groups by addition only

2009-11-16

arxiv.org/abs/0911.2966v1

Forum Math. 21 (2009), no. 1, 23--41

Mathematics

Group Theory

Scientific paper

We define the positive diameter of a finite group $G$ with respect to a generating set $A\subset G$ to be the smallest non-negative integer $n$ such that every element of $G$ can be written as a product of at most $n$ elements of $A$. This invariant, which we denote by $\diam_A^+(G)$, can be interpreted as the diameter of the Cayley digraph induced by $A$ on $G$. In this paper we study the positive diameters of a finite abelian group $G$ with respect to its various generating sets $A$. More specifically, we determine the maximum possible value of $\diam_A^+(G)$ and classify all generating sets for which this maximum value is attained. Also, we determine the maximum possible cardinality of $A$ subject to the condition that $\diam_A^+(G)$ is "not too small". Conceptually, the problems studied are closely related to our earlier work and the results obtained shed a new light on the subject. Our original motivation came from connections with caps, sum-free sets, and quasi-perfect codes.

Affiliated with

Also associated with

No associations

Rating

Generating abelian groups by addition only 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 Generating abelian groups by addition only, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generating abelian groups by addition only will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-498867