A new upper bound for the cross number of finite Abelian groups

Details A new upper bound for the cross number of finite Abelian groups A new upper bound for the cross number of finite Abelian groups

2007-12-03

arxiv.org/abs/0712.0331v1

Israel Journal of Mathematics 172 (2009) 253-278

Mathematics

Number Theory

21 pages, to appear in Israel Journal of Mathematics

Scientific paper

10.1007/s11856-009-0072-3

In this paper, building among others on earlier works by U. Krause and C. Zahlten (dealing with the case of cyclic groups), we obtain a new upper bound for the little cross number valid in the general case of arbitrary finite Abelian groups. Given a finite Abelian group, this upper bound appears to depend only on the rank and on the number of distinct prime divisors of the exponent. The main theorem of this paper allows us, among other consequences, to prove that a classical conjecture concerning the cross and little cross numbers of finite Abelian groups holds asymptotically in at least two different directions.

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