On the K-Ring of the Classifying Space of the Generalized Quaternion Group

TL;DR

This paper characterizes the K-theory ring of the classifying space for generalized quaternion groups, providing generators, relations, and the order of key elements in truncated rings.

Contribution

It offers a detailed algebraic description of the K-ring for these classifying spaces, including minimal relations and generator orders, advancing understanding in algebraic topology.

Findings

Explicit generators and relations for the K-ring.

Computed the order of the main generator in truncated rings.

Enhanced the algebraic understanding of classifying spaces for quaternion groups.

Abstract

We describe the K-ring of the classifying space of the generalized quaternion group in terms of generators and the minimal set of relations. We also compute the order of the main generator in the truncated rings.