Length of the Group Algebra of the Direct Product of a Cyclic Group and a Cyclic P-Group in the Modular Case
摘要
In this paper, the length of the group algebra of the direct product of a cyclic group and a cyclic p-group over a field of characteristic p is determined. A general lower bound for the length of a commutative group algebra is proved. It is shown that in the case of the direct product of a cyclic group and a cyclic p-group this bound is sharp.