Rendiconti del Seminario Matematico della Università di Padova
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Published online: 2010-06-30
Structure and Detection Theorems for $k[C_2\times C_4]$-ModulesSemra Öztürk Kaptanoglu (1) 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 availableonly when G is cyclic, Cpn, or C2×C2.Tackling the first interesting case, namely modules over k[C2×C4], some structure theorems revealing the differences between elementary and non-elementary abelian group cases are obtained.The shifted cyclic subgroups of k[C2×C4] are characterized.Using the direct sum decompositions of the restrictions of a k[C2×C2]-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[C2×C4]-modules having the same rank variety as k[C2×C2]-modulescan be detected by the set of multiplicities,where C2×C2is the unique maximal elementary abelian subgroup of C2×C4.
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Öztürk Kaptanoglu Semra: Structure and Detection Theorems for $k[C_2\times C_4]$-Modules. Rend. Sem. Mat. Univ. Padova 123 (2010), 169-189. doi: 10.4171/RSMUP/123-8