This research delves into the intricate structure of conjugacy classes within finitely generated groups possessing small cancellation properties. Focusing on groups derived from the free group on two generators () through small cancellation theory, the study explores the interplay between small cancellation conditions, conjugacy classes, and their implications for the group’s geometry. Residually finite groups, quasi-isometry, and the impact of varying parameters in small cancellation conditions are key aspects considered. The investigation aims to provide a comprehensive understanding of how these factors contribute to the diversity of conjugacy classes and their significance within this class of groups.
Keywords: conjugacy classes, finitely generated groups, free group on two generators (F_2), quasi-isometry, residually finite groups, small cancellation theory
