Structure and Detection Theorems for -Modules

  • Semra Öztürk Kaptanoglu

    Middle East Technical University, Ankara, Turkey


Let k[G] be the group algebra, where G is a finite abelian p-group and k is a field of characteristic p. A complete classification of finitely generated k[G]-modules is available only when G is cyclic, Cpn, or _C_2×_C_2. Tackling the first interesting case, namely modules over k[_C_2×_C_4], some structure theorems revealing the differences between elementary and non-elementary abelian group cases are obtained. The shifted cyclic subgroups of k[_C_2×_C_4] are characterized. Using the direct sum decompositions of the restrictions of a k[_C_2×_C_2]-module M to shifted cyclic subgroups we define the set of multiplicities of M. It is an invariant richer than the rank variety. Certain types of k[_C_2×_C_4]-modules having the same rank variety as k[_C_2×_C_2]-modules can be detected by the set of multiplicities, where _C_2×_C_2 is the unique maximal elementary abelian subgroup of _C_2×_C_4.

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