On the number of subgroups of finite abelian groups
Journal de Théorie des Nombres de Bordeaux, Volume 9 (1997) no. 2, pp. 371-381.

Let T(x)=K 1 xlog 2 x+K 2 xlogx+K 3 x+Δ(x), where T(x) denotes the number of subgroups of all abelian groups whose order does not exceed x and whose rank does not exceed 2, and Δ(x) is the error term. It is proved that 1 X Δ 2 (x)dxX 2 log 31/3 X, 1 X Δ 2 (x)dx=Ω(X 2 log 4 X).

Soit T(x)=K 1 xlog 2 x+K 2 xlogx+K 3 x+Δ(x),T(x) désigne le nombre de sous groupes des groupes abéliens dont l’ordre n’excède pas x et dont le rang n’excède pas 2, et Δ(x) est le terme d’erreur. On démontre que 1 X Δ 2 (x)dxX 2 log 31/3 X, 1 X Δ 2 (x)dx=Ω(X 2 log 4 X).

DOI: 10.5802/jtnb.208
Classification: 11N45,  11L07,  20K01,  20K27
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Aleksandar Ivić. On the number of subgroups of finite abelian groups. Journal de Théorie des Nombres de Bordeaux, Volume 9 (1997) no. 2, pp. 371-381. doi : 10.5802/jtnb.208. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.208/

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