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Can I read Generating Abelian Groups by Addition Only on EtoBox?
Generating Abelian Groups by Addition Only by Benjamin Klopsch; Vsevolod F. Lev is a Mathematics article available to read on EtoBox.
What is Generating Abelian Groups by Addition Only about?
We define the positive diameter of a finite group G with respect to a generating set A J 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 þ A ðGÞ, 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 þ A ðGÞ 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 þ A ðGÞ is ''not too small''. Conceptually, the problems studied are closely related to our earlier work [7] 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.
Who reads Generating Abelian Groups by Addition Only?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Benjamin Klopsch; Vsevolod F. Lev
- Publisher
- Walter de Gruyter GmbH
- Published
- 2009
- Language
- EN
- Field
- Mathematics (Physical Sciences)