2015/05/23 by Waldemar Hołubowski, Waldemar Holubowski, Holubowski, Waldemar +2
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Finite Group Theory Research #math.GR #msc:20F12 #msc:20F14
paper · pdf · doi:10.48550/arxiv.1505.06355
arxiv created 2015/05/23 · arxiv updated 2015/05/26
We complete characterization of bijections preserving commutators (PC-maps) in the group of unitriangular matrices UT(n,F) over a field F, where n is a natural number or infinity. PC-maps were recently described up to almost identity PC-maps by M.Chen, D.Wang, and H.Zhai (2011) for finite n and by R.Slowik (2013) for n=∞. An almost identity map is a map, preserving elementary transvections. We show that an almost identity PC-map is a multiplication by a central element. In particular, if n=∞, then an almost identity map is identity. Together with the result of R.Slowik this shows that any PC-map of UT(∞, F) is an automorphism.