Zeta and normal zeta functions for a subclass of space groups

TL;DR

This paper computes zeta and normal zeta functions for a specific subclass of space groups with cyclic point groups of order 2, providing formulas to count subgroups and normal subgroups of given indices.

Contribution

It introduces explicit calculations of zeta functions for space groups with cyclic order 2 point groups, advancing subgroup enumeration methods.

Findings

Derived formulas for zeta functions of these space groups

Determined subgroup counts of various indices

Provided explicit enumeration techniques

Abstract

We calculate zeta and normal zeta functions of space groups with the point group isomorphic to the cyclic group of order 2. The obtained results are applied to determine the number of subgroups, resp. normal subgroups, of a given index for each of these groups.