Structure and Detection Theorems for -Modules

  • Semra Öztürk Kaptanoglu

    Middle East Technical University, Ankara, Turkey


Let be the group algebra, where is a finite abelian -group and is a field of characteristic . A complete classification of finitely generated -modules is available only when is cyclic, , or . Tackling the first interesting case, namely modules over , some structure theorems revealing the differences between elementary and non-elementary abelian group cases are obtained. The shifted cyclic subgroups of are characterized. Using the direct sum decompositions of the restrictions of a -module to shifted cyclic subgroups we define the set of multiplicities of . It is an invariant richer than the rank variety. Certain types of -modules having the same rank variety as -modules can be detected by the set of multiplicities, where is the unique maximal elementary abelian subgroup of .

Cite this article

Semra Öztürk Kaptanoglu, Structure and Detection Theorems for -Modules. Rend. Sem. Mat. Univ. Padova 123 (2010), pp. 169–189

DOI 10.4171/RSMUP/123-8