On Butler's Unimodality Result

denote the number of subgroups of order in a finite abelian p-group of type λ. Then is a polynomial in p with nonnegative coefficients, which depends only on λ and i. Butler proved that where has nonnegative coefficients. We prove this fact by using formulas shown by Stehling.

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Received: August 5, 1997

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Takegahara, Y. On Butler's Unimodality Result. Combinatorica 18, 437–439 (1998). https://doi.org/10.1007/PL00009832

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  • AMS Subject Classification (1991) Classes:  20K01