Cohen-Macaulay types of subgroup lattices of finite abelian \(p\)-groups
type: Item
instance of: scholarly article
title: Cohen-Macaulay types of subgroup lattices of finite abelian \(p\)-groups
zbMATH Open document ID: 0838.13016
DOI: 10.1007/BF01793015
author: Hideaki Morita
published in: Graphs and Combinatorics
publication date: 1996-06-09T00:00:00Z
review text: This paper focusses on a special type of Stanley-Reisner rings, namely on those with simplicial complex obtained from the subgroup lattice \(L(G)\) of a finite Abelian \(p\)-group associated with a given partition; it is denoted by \(k[L(G)]\). As is known, by the modularity of \(L(G)\), \(k[L(G)]\) is Cohen-Macaulay and its Cohen-Macaulay type (the last Betti number) can be calculated by means of the Möbius function of \(L(G)\). The main part of the paper consists in grasping that function in more detail, culminating finally in the result, that the Cohen-Macaulay type of \(k[L(G)]\) is a polynomial in \(p\) with integer coefficients.
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 20D30
Mathematics Subject Classification ID: 05E15
Mathematics Subject Classification ID: 55U10
zbMATH DE Number: 811349
zbMATH Keywords: Stanley-Reisner rings
zbMATH Keywords: Cohen-Macaulay type
reviewed by: Gerhard Kowol
MaRDI profile type: Publication
cites work: Subgroups of Abelian Groups
cites work: Q4274969
cites work: A Unimodality Result in the Enumeration of Subgroups of a Finite Abelian Group
cites work: Cohen-Macaulay types of Cohen-Macaulay complexes
cites work: Q3947818
cites work: Q3748279
full work available at URL: https://doi.org/10.1007/bf01793015
OpenAlex ID: W1991251322
description: scientific article; zbMATH DE number 811349