A new upper bound for the cross number of finite abelian groups
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...
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| Veröffentlicht in: | Israel journal of mathematics 2009, Vol.172 (1), p.253-278 |
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| container_title | Israel journal of mathematics |
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| creator | Girard, Benjamin |
| description | 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. |
| doi_str_mv | 10.1007/s11856-009-0072-3 |
| format | Article |
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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. 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| ispartof | Israel journal of mathematics, 2009, Vol.172 (1), p.253-278 |
| issn | 0021-2172 1565-8511 |
| language | eng |
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| subjects | Algebra Analysis Applications of Mathematics Combinatorics Group Theory Group Theory and Generalizations Mathematical and Computational Physics Mathematics Number Theory Theoretical Upper bounds |
| title | A new upper bound for the cross number of finite abelian groups |
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