Israel Journal of Mathematics

, Volume 172, Issue 1, pp 253–278 | Cite as

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

Article

Abstract

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 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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Copyright information

© Hebrew University Magnes Press 2009

Authors and Affiliations

  1. 1.Centre de Mathématiques Laurent SchwartzUMR 7640 du CNRS École polytechniquePalaiseau CedexFrance

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