MSI-2000: Multivariate statistical analysis in honor of Professor Minoru Siotani on his 70th birthday: T. Hayakawa, M. Aoshima, K. Shimizu and V. Taneja, eds. American Sciences Press, Inc., $125.00, 236 pages

Abstract

We study the maximal cross number K(G) of a minimal zero-sum sequence and the maximal cross number k(G) of a zero-sum free sequence over a finite abelian group G, defined by Krause and Zahlten. In the first part of this paper, we extend a previous result by X. He to prove that the value of k(G) conjectured by Krause and Zahlten holds for G⨁Cpa⨁Cpb when it holds for G, provided that p and the exponent of G are related in a specific sense. In the second part, we describe a new method for proving that the conjectured value of K(G) holds for abelian groups of the form Hp⨁Cqm (where Hp is any finite abelian p-group) and Cp⨁Cq⨁Cr for any distinct primes p,q,r. We also give a structural result on the minimal zero-sum sequences that achieve this value.