Structure and Detection Theorems for -Modules
Semra Öztürk Kaptanoglu
Middle East Technical University, Ankara, Turkey
![Structure and Detection Theorems for $k[C_2\times C_4]$-Modules cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserials%2Fcover-rsmup.png&w=3840&q=90)
Abstract
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 availableonly 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]-modulescan be detected by the set of multiplicities,where _C_2×_C_2is 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