The central heights of stability groups of series in vector spaces
Czechoslovak Mathematical Journal (2016)
- Volume: 66, Issue: 1, page 213-222
- ISSN: 0011-4642
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topWehrfritz, Bertram A. F.. "The central heights of stability groups of series in vector spaces." Czechoslovak Mathematical Journal 66.1 (2016): 213-222. <http://eudml.org/doc/276760>.
@article{Wehrfritz2016,
abstract = {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.},
author = {Wehrfritz, Bertram A. F.},
journal = {Czechoslovak Mathematical Journal},
keywords = {central height; linear group; stability group},
language = {eng},
number = {1},
pages = {213-222},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The central heights of stability groups of series in vector spaces},
url = {http://eudml.org/doc/276760},
volume = {66},
year = {2016},
}
TY - JOUR
AU - Wehrfritz, Bertram A. F.
TI - The central heights of stability groups of series in vector spaces
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 1
SP - 213
EP - 222
AB - 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.
LA - eng
KW - central height; linear group; stability group
UR - http://eudml.org/doc/276760
ER -
References
top- Casolo, C., Puglisi, O., 10.1016/j.jalgebra.2012.06.028, J. Algebra 370 (2012), 133-151. (2012) Zbl1279.20067MR2966831DOI10.1016/j.jalgebra.2012.06.028
- Robinson, D. J. S., Finiteness Conditions and Generalized Soluble Groups. Part 1, Springer Berlin (1972). (1972) MR0332989
- Robinson, D. J. S., Finiteness Conditions and Generalized Soluble Groups. Part 2, Springer Berlin (1972). (1972) MR0332990
- Traustason, G., 10.1016/j.jalgebra.2014.11.023, J. Algebra 425 (2015), 31-41. (2015) Zbl1317.20047MR3295976DOI10.1016/j.jalgebra.2014.11.023
- Wehrfritz, B. A. F., 10.1016/j.jalgebra.2015.09.006, J. Algebra 445 (2016), Article ID 15414, 352-364. (2016) Zbl1374.20041MR3418062DOI10.1016/j.jalgebra.2015.09.006
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