Shved, Daniil On the structure of groups of virtually trivial automorphisms. (English) Zbl 1368.20039 Commun. Algebra 45, No. 5, 1842-1852 (2017). Summary: If \(G\) is an arbitrary group, then the group \(\operatorname{Aut}_{vt}(G)\) consists, by definition, of all virtually trivial automorphisms of \(G\), i.e. of all automorphisms that have the fixed-point subgroup of finite index in \(G\). We investigate the structure of \(\operatorname{Aut}_{vt}(G)\) and show that it possesses a certain “well-behaved” normal series which demonstrates its closeness to finitary linear groups. This is then used to prove that each simple section of \(\operatorname{Aut}_{vt}(G)\) is a finitary linear group. Cited in 1 Document MSC: 20F28 Automorphism groups of groups 20E36 Automorphisms of infinite groups 20F50 Periodic groups; locally finite groups 20F14 Derived series, central series, and generalizations for groups 20F19 Generalizations of solvable and nilpotent groups 20G15 Linear algebraic groups over arbitrary fields Keywords:finitary linear groups; finitary permutation groups; \(p\)-groups; virtually trivial automorphisms PDFBibTeX XMLCite \textit{D. Shved}, Commun. Algebra 45, No. 5, 1842--1852 (2017; Zbl 1368.20039) Full Text: DOI References: [1] DOI: 10.1007/BF00750846 · Zbl 0840.20038 [2] Belyaev, V. V., Shved, D. A. (2009). Finitary automorphisms of groups.Proc. Steklov Inst. Math.267(suppl.1):S49–S56. · Zbl 1238.20048 [3] DOI: 10.1134/S000143461103031X · Zbl 1236.20041 [4] DOI: 10.1142/2386 [5] DOI: 10.1007/978-94-011-0329-9_6 [6] Menegazzo F., Rend. Sem. Mat. Univ. Padova 78 pp 267– (1987) [7] DOI: 10.1007/978-1-4419-8594-1 [8] DOI: 10.1007/BF01238708 · Zbl 0294.20030 [9] Shved D. A., Trudy Inst. Mat. i Mekh. UrO RAN 17 (4) pp 312– (2011) [10] Zalesskiĭ A. E., Dokl. Akad. Nauk BSSR 19 (8) pp 681– (1975) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.