Abstract
Let phi be a self-map of the symmetric group S_Omega acting on a countable set Omega . We show in an elementary fashion that if phi has the property that sigma tau is conjugate to phi (sigma )phi (tau ) for every choice of sigma ,tau in S_Omega , then it is necessarily an automorphism or an antiautomorphism of S_Omega . As a corollary to this result, the so-called 2-local automorphisms of S_Omega are also described.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
