Cohen-Macaulay types of subgroup lattices of finite abelian \(p\)-groups (Q1900524)

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.