Zeta functions of integral representations of cyclic p-groups

JOURNAL OF ALGEBRA

卷:274

Article

Wittmann, C

关键词: zeta function;    modules over group rings;    integral representation;    Mobius function;   

DOI  :  10.1016/S0021-8693(03)00422-8

来源: Elsevier

【 摘 要 】

For a prime number p and C-pk, the cyclic group of order p(k), we consider the group ring Z(p)[C-pk] over the p-adic integers. Following L. Solomon, one can define the zeta function of the free Z(p) [C-pk]-module Z(p)[C-pk](n), which counts submodules of finite index in Z(p)[C-pk](n). In this article we develop a recursion formula (relating submodules of Z(p)[C-pk](n) to certain submodules of Z(p)[Cpk-1](n) ),(.)which yields some new explicit formulas for the zeta function of Z(p)[C-pk](n) in the cases k = 1, 2 and n greater than or equal to 1, and k = 3, n = 1. An important combinatorial tool for these computations is the Mobius function of a partially ordered set. (C) 2004 Published by Elsevier Inc.

【 授权许可】

Free