Note on the conjugacy classes of elements and their centralizers for the free product of two groups

TL;DR

This paper characterizes conjugacy classes and centralizers in free products of groups, correcting previous calculations of their group ring's cyclic homology.

Contribution

It provides a detailed description of conjugacy classes and centralizers in free products, and rectifies earlier homology computations.

Findings

Corrected the calculation of cyclic and periodic cyclic homology for free product group rings.

Described conjugacy classes and centralizers explicitly for free products.

Enhanced understanding of algebraic structures in free product groups.

Abstract

We describe the conjugacy classes of the elements of the free product of two groups and their centralizers and, as a consequence, we correct the calculation of the cyclic and periodic cyclic homology of the group ring of the free product of two groups given in a previous paper.