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Keywords:
central height; linear group; stability group
central height; linear group; stability group
Summary:
We compute the central heights of the full stability groups $S$ of ascending series and of descending series of subspaces in vector spaces over fields and division rings. The aim is to develop at least partial right analogues of results on left Engel elements and related nilpotent radicals in such $S$ proved recently by Casolo \& Puglisi, by Traustason and by the current author. Perhaps surprisingly, while there is an absolute bound on these central heights for descending series, for ascending series the central height can be any ordinal number.
References:
[1] Casolo, C., Puglisi, O.: Hirsch-Plotkin radical of stability groups. J. Algebra 370 (2012), 133-151. DOI 10.1016/j.jalgebra.2012.06.028 | MR 2966831 | Zbl 1279.20067
[2] Robinson, D. J. S.: Finiteness Conditions and Generalized Soluble Groups. Part 1. Springer Berlin (1972). MR 0332989
[3] Robinson, D. J. S.: Finiteness Conditions and Generalized Soluble Groups. Part 2. Springer Berlin (1972). MR 0332990
[4] Traustason, G.: On the Hirsch-Plotkin radical of stability groups. J. Algebra 425 (2015), 31-41. DOI 10.1016/j.jalgebra.2014.11.023 | MR 3295976 | Zbl 1317.20047
[5] Wehrfritz, B. A. F.: Stability groups of series in vector spaces. J. Algebra 445 (2016), Article ID 15414, 352-364. DOI 10.1016/j.jalgebra.2015.09.006 | MR 3418062 | Zbl 1374.20041
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