Normal automorphisms of the metabelian product of free abelian Lie algebras
Algebra and discrete mathematics, Tome 30 (2020) no. 2, pp. 230-234
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Let $M$ be the metabelian product of free abelian Lie algebras of finite rank. In this study we prove that every normal automorphism of $M$ is an $\mathrm{IA}$-automorphism and acts identically on $M'$.
Keywords:
free abelian Lie algebras, metabelian product, automorphisms.
@article{ADM_2020_30_2_a5,
author = {N. \c{S}. \"O\u{g}\"u\c{s}l\"u},
title = {Normal automorphisms of the metabelian product of free abelian {Lie} algebras},
journal = {Algebra and discrete mathematics},
pages = {230--234},
year = {2020},
volume = {30},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ADM_2020_30_2_a5/}
}
N. Ş. Öğüşlü. Normal automorphisms of the metabelian product of free abelian Lie algebras. Algebra and discrete mathematics, Tome 30 (2020) no. 2, pp. 230-234. http://geodesic.mathdoc.fr/item/ADM_2020_30_2_a5/
[1] G. Endimioni, “Normal automorphisms of a free metabelian nilpotent group”, Glasgow Math. J., 52 (2010), 169–177 | DOI | MR | Zbl
[2] Ş. F{\i}nd{\i}k, “Normal and normally outer automorphisms of free metabelian nilpotent Lie algebras”, Serdica Math. J., 36 (2010), 171–210 | MR | Zbl
[3] N. Ş. Öğüşlü, “IA-automorphisms of a solvable product of abelian Lie algebras”, Int. J. Sci. Research Pub., 8:4 (2018), 84–85
[4] V. A. Romankov, “Normal automorphisms of discrete groups”, Siberian Math. J., 24:4 (1983), 604–614 | DOI | MR | Zbl
[5] E. I. Timoshenko, “Normal automorphisms of a soluble product of abelian groups”, Siberian Math. J., 56:1 (2015), 191–198 | DOI | MR | Zbl