Let FG be the group ring of a group G over a field F. We consider the group of unitary units of FG with respect to the classical involution. Under suitable restrictions upon F, we show that if the unitary units of FG are both bounded Engel and solvable, then the entire unit group of FG is nilpotent. This extends a result of Fisher, Parmenter and Sehgal.
Bounded Engel and solvable unitary units in group rings / Lee, Gregory T.; Sehgal, Sudarshan K.; Spinelli, Ernesto. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 501:(2018), pp. 225-232. [10.1016/j.jalgebra.2017.12.021]
Bounded Engel and solvable unitary units in group rings
Lee, Gregory T.;Spinelli, Ernesto
2018
Abstract
Let FG be the group ring of a group G over a field F. We consider the group of unitary units of FG with respect to the classical involution. Under suitable restrictions upon F, we show that if the unitary units of FG are both bounded Engel and solvable, then the entire unit group of FG is nilpotent. This extends a result of Fisher, Parmenter and Sehgal.File allegati a questo prodotto
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