Generalized flags in p-groups

If mu, lambda are partitions of n, denote by L-mu, L-lambda the subgroup la ttices of abelian p-groups of types mu, lambda, respectively. This paper st udies conditions for the existence of order preserving injections ("general ized Bags") from L-mu into L-lambda. Butler has shown by topological method s that "mu dominates lambda" is necessary. Here algebraic and combinatorial methods are used to obtain further conditions both for this problem and fo r the closely related one where abelian p-groups are replaced by F-p vector spaces with nilpotent linear transformations. (C) 2000 Elsevier Science Lt d. All rights reserved.