Let F be a field of characteristic different from 2 and G a group. Under the classical involution on the group ring FG, we show that if FG is modular, then the group of unitary units of FG is nilpotent if and only if the entire unit group is nilpotent. We also demonstrate that this does not necessarily hold if FG is not modular, but it is still true if F is algebraically closed.
Group rings whose unitary units are nilpotent / Gregory T., Lee; Sudarshan K., Sehgal; Spinelli, Ernesto. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 410:(2014), pp. 343-354. [10.1016/j.jalgebra.2014.01.041]
Group rings whose unitary units are nilpotent
SPINELLI, ERNESTO
2014
Abstract
Let F be a field of characteristic different from 2 and G a group. Under the classical involution on the group ring FG, we show that if FG is modular, then the group of unitary units of FG is nilpotent if and only if the entire unit group is nilpotent. We also demonstrate that this does not necessarily hold if FG is not modular, but it is still true if F is algebraically closed.File allegati a questo prodotto
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
