Abstract
Let F be an infinite field of characteristic , G be a group, and be an involution of G extended linearly to an involution of the group algebra FG. In the literature, group identities on units and on symmetric units have been considered. Here, we investigate normalized Laurent polynomial identities (as a generalization of group identities) on under the conditions that either p > 2 or F is algebraically closed. For instance, we show that if G is torsion and satisfies a normalized Laurent polynomial identity, then satisfies a group identity and FG satisfies a polynomial identity.
Acknowledgments
The authors would like to thank the referee for valuable comments and suggestions.
Data availability statement
Data sharing is not applicable to this article as no datasets or any other materials were generated or analyzed during the current study.
Disclosure statement
The authors have no competing interests to declare that are relevant to the content of this article. The authors declare no conflict of interest.