turkmath.org

Let $A$ be an abelian $p$-group of exponent $p^t$, and k be an algebraically closed field of characteristic $p$. Since there is no classification for indecomposable modules over $k[A]$ except for cyclic groups, and the group $Z_2 x Z_2$, these modules are studied via restrictions to subalgebras corresponding to the cyclic subgroups of the unit group of $k[A]$. This approach became useful especially after the definition of modules of constant Jordan type. We define the class of restricted $k[A]$-modules of constant $p^t$-Jordan type, generalize several theorems by Benson, and verify a generalization of conjectures by Suslin and Rickard.