Bi‐orderability and generalized torsion elements from the perspective of profinite properties

Key Points

• The study aims to explore the relationship between bi-orderable groups and profinite properties, particularly focusing on generalized torsion elements.
• Constructed bi-orderable groups using fiber products from left-orderable groups.
• Analyzed the implications of bi-orderability on profinite properties.
• Examined the presence of generalized torsion elements in relation to profinite characteristics.
• Bi-orderability is established as not a profinite property.
• It is confirmed that the existence of generalized torsion elements also does not constitute a profinite property.