Generalized flags in p-groups

If μ, λ are partitions of n, denote by Lμ, Lλ the subgroup lattices of abelian p-groups of types μ, λ respectively. This paper studies conditions for the existence of order preserving injections (“generalized flags”) from Lμ into Lλ. Butler has shown by topological methods that “μ dominates λ” is necessary. Here algebraic and combinatorial methods are used to obtain further conditions both for this problem and for the closely related one where abelian p-groups are replaced by p vector spaces with nilpotent linear transformations.