Discrete valuation rings, partitions and p-groups I

A finite abelian p-group with an automorphism x such that 1 + center dot center dot center dot + xp-1 = 0, can be viewed as a module over an appropriate discrete valuation ring O containing Zp (the ring of p-adic integer). This yields the natural problem of comparing the invariants of A as a Zp-module to its invariants as an O-module. We solve the latter problem in a more general setting and give some applications to the structure of some p-groups and their automorphisms.(c) 2023 Elsevier B.V. All rights reserved.