Cross Number

The cross number of a zero-system sigma={g_1,g_2,...,g_n} of G is defined as


The cross number of a group G has two different definitions.

1. Anderson and Chapman (2000) define the cross number of G as K(G)=max{k(sigma):sigma in U(G)}.

2. Chapman (1997) defines K(G)=exp(G)·max{k(sigma):sigma in U(G)}, where exp(G)=LCM{|g|:g in G}.

A value of the cross number: for a prime p and n in Z^+, K(Z_(p^n))=p^n=exp(G). A stronger statement is that any finite Abelian group G is cyclic of prime power order iff K(G)=exp(G).

This entry contributed by Nick Hutzler

Explore with Wolfram|Alpha


Anderson, D. F. and Chapman, S. T. "On the Elasticities of Krull Domains with Finite Cyclic Divisor Class Group." Comm. Alg. 28, 2543-2553, 2000.Chapman, S. T. "On the Davenport Constant, the Cross Number, and Their Applications in Factorization Theory." In Zero-Dimensional Commutative Rings (Ed. D. F. Anderson and D. E. Dobbs). New York: Dekker, pp. 167-190, 1997.

Referenced on Wolfram|Alpha

Cross Number

Cite this as:

Hutzler, Nick. "Cross Number." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

Subject classifications