Abstract
Let F be a field, T n the group consisting of all n × n invertible upper triangular matrices over F. In this article we classify bijective maps ϕ from T n to itself satisfying ϕ[x, y] = [ϕ(x), ϕ(y)]. We show that each such map differs only slightly from an automorphism of T n .
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Babich M, Bobenko A. Willmore tori with umbilic lines and minimal surfaces in hyperbolic space. Duke Math J, 1993, 72: 151–185
Baribeau L, Ransford T. Non-linear spectrum-preserving maps. Bull London Math Soc, 2000, 32: 8–14
Li C K, Pierce S. Linear preserver problem. Amer Math Monthly, 2001, 108: 591–605
Li C K, Tsing N K. Linear preserver problem: a brief introduction and some special techniques. Linear Algebra Appl, 1992, 162–164: 217–235
Marcus M. Linear operations of matrices. Amer Math Monthly, 1962, 69: 837–847
Pierce S, et al. A survey of linear preserver problems. Linear Multilinear Algebra, 1992, 33: 1–192
Radjavi H, Šemrl P. Non-linear maps preserving solvability. J Algebra, 2004, 280: 624–634
Šemrl P. Non-linear commutativity preserving maps. Acta Sci Math (Szeged), 2005, 71: 781–819
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, D., Ou, S. & Zhang, W. Bijective maps preserving commutators on a solvable classical group. Sci. China Math. 53, 1723–1730 (2010). https://doi.org/10.1007/s11425-010-3133-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11425-010-3133-5