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- W4295250524 abstract "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 $n=infty$. 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 $n=infty$, then an almost identity map is identity. Together with the result of R.Slowik this shows that any PC-map of $UT(infty, F)$ is an automorphism." @default.
- W4295250524 created "2022-09-12" @default.
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- W4295250524 date "2015-05-23" @default.
- W4295250524 modified "2023-10-17" @default.
- W4295250524 title "Bijections preserving commutators and automorphisms of unitriangular group" @default.
- W4295250524 doi "https://doi.org/10.48550/arxiv.1505.06355" @default.
- W4295250524 hasPublicationYear "2015" @default.
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