p-Power Points and Modules of Constant p-Power Jordan Type

Abstract

We study finitely generated modules over k[G] for a finite abelian p-group G, char(k) = p, through restrictions to certain subalgebras of k[G]. We define p-power points, shifted cyclic p-power order subgroups of k[G], and give characterizations of these. We define modules of constant p ^t -Jordan type, constant p ^t -power-Jordan type as generalizations of modules of constant Jordan type, and p ^t -support, nonmaximal p ^t -support spaces. We obtain a filtration of modules of constant Jordan type with modules of constant p-power Jordan type as the last term and give examples of non-isomorphic modules of constant p-power Jordan type having the same constant Jordan type.

Key Words:

• Constant Jordan type
• Constant p-power Jordan type
• Modular representation
• p-Point
• p-Power point
• Restriction
• Shifted cyclic subgroup
• Wild representation type

2000 Mathematics Subject Classification:

• Primary 20C05, 13C05
• Secondary 20C20, 16G10

ACKNOWLEDGMENT

I thank very much an anonymous referee for valuable suggestions improving the article.

Notes

Communicated by D. Nakano.