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The cross number of finite Abelian groups. III. (English) Zbl 0848.20048

Summary: We continue our investigations on the cross number \(K(G)\) of a finite abelian group \(G\) [for part II cf. Eur. J. Comb. 15, No. 4, 399-405 (1994; Zbl 0833.20061)]. In Section 1 we refine the crucial inequality \(K^*(G)\leq K(G)\), introduce some variants of \(K(G)\) and study their properties. In Section 2 we derive an upper bound for the cross number.

MSC:

20K01 Finite abelian groups
20D60 Arithmetic and combinatorial problems involving abstract finite groups

Citations:

Zbl 0833.20061
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References:

[1] Alford, W.R.; Granville, A.; Pomerance, C., There are infinitely many Carmichael numbers, Ann. math., 140, 703-722, (1994) · Zbl 0816.11005
[2] P. van Emde Boas and D. Kruyswijk, A combinatorial problem on finite abelian groups III, Report ZW-1969-08, Math. Centre Amsterdam. · Zbl 0245.20046
[3] Geroldinger, A., The cross number of finite abelian groups, J. number theory, 48, 219-223, (1994) · Zbl 0814.20033
[4] Geroldinger, A.; Schneider, R., The cross number of finite abelian groups II, Eur. J. combin., 15, 399-405, (1994) · Zbl 0833.20061
[5] Jungnickel, D., Finite fields, BI-wissenschaftsverlag, (1993)
[6] Krause, U., A characterization of algebraic number fields with cyclic class group of prime power order, Math. Z., 186, 143-148, (1984) · Zbl 0522.12006
[7] Krause, U.; Zahlten, C., Arithmetic in Krull monoids and the cross number of divisor class groups, Mitteilungen d. math. gesellschaft Hamburg, 12, 681-696, (1991) · Zbl 0756.20010
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