## 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

### Keywords:

cross number; finite Abelian groups

Zbl 0833.20061
Full Text:

### References:

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