Rendiconti del Seminario Matematico della Università di Padova

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Volume 123, 2010, pp. 169–189
DOI: 10.4171/RSMUP/123-8

Structure and Detection Theorems for $k[C_2\times C_4]$-Modules

Semra Öztürk Kaptanoglu[1]

(1) Department of Mathematics, Middle East Technical University, 06531, 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 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]-modules can be detected by the set of multiplicities, where C2×C2 is 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