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Cohen-Macaulay types of subgroup lattices of finite abelianp-groups

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Abstract

For a minimal free resolution of a Stanley-Reisner ring constructed from the order complex of a modular lattice. T. Hibi showed that its last Betti number (called the Cohen-Macaulay type) is computed by means of the Möbius function of the given modular lattice. Using this result, we consider the Stanley-Reisner ring of the subgroup lattice of a finite abelianp-group associated with a given partition, and show that its Cohen-Macaulay type is a polynomial inp with integer coefficients.

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  1. Department of Mathematics, Faculty of Science, Hokkaido University, 060, Sapporo, Japan

    Hideaki Morita

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  1. Hideaki Morita
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Morita, H. Cohen-Macaulay types of subgroup lattices of finite abelianp-groups. Graphs and Combinatorics 11, 275–283 (1995). https://doi.org/10.1007/BF01793015

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  • DOI: https://doi.org/10.1007/BF01793015

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