gyrogroups: generalization of groups

A gyrogroup is a non-associative algebraic structure, which is anatural generalization of a group, arising from the study of the parametriza-tion of the lorentz transformation group by abraham a. ungar. gyrogroupsshare many properties with groups and, in fact, every group may be viewed asa gyrogroup with trivial gyroautomorphisms. in this talk, we indicate strongconnections between gyrogroups and classical structures such as groups, lin-ear spaces, topological spaces, and metric spaces from the algebraic point ofview.