Memoirs of the American Mathematical Society 1994; 160 pp; softcover Volume: 112 ISBN10: 082182600X ISBN13: 9780821826003 List Price: US$42 Individual Members: US$25.20 Institutional Members: US$33.60 Order Code: MEMO/112/539
 This work presents foundational research on two approaches to studying subgroup lattices of finite abelian \(p\)groups. The first approach is linear algebraic in nature and generalizes Knuth's study of subspace lattices. This approach yields a combinatorial interpretation of the Betti polynomials of these CohenMacaulay posets. The second approach, which employs HallLittlewood symmetric functions, exploits properties of Kostka polynomials to obtain enumerative results such as rankunimodality. Butler completes Lascoux and Schützenberger's proof that Kostka polynomials are nonnegative, then discusses their monotonicity result and a conjecture on Macdonald's twovariable Kostka functions. Readership Research mathematicians. Table of Contents  Introduction
 Subgroups of finite Abelian groups
 HallLittlewood symmetric functions
 Some enumerative combinatorics
 Some algebraic combinatorics
