02929nam 22005415 450 991104781110332120251120120403.09783032046208(electronic bk.)978303204619210.1007/978-3-032-04620-8(MiAaPQ)EBC32422140(Au-PeEL)EBL32422140(CKB)43552486100041(DE-He213)978-3-032-04620-8(EXLCZ)994355248610004120251120d2025 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierGroup Identities on Units and Symmetric Units of Group Rings /by Gregory T. Lee2nd ed. 2025.Cham :Springer Nature Switzerland :Imprint: Springer,2025.1 online resource (486 pages)Algebra and Applications,2192-2950 ;33Print version: Lee, Gregory T. Group Identities on Units and Symmetric Units of Group Rings Cham : Springer London, Limited,c2025 9783032046192 Group Identities on Units of Group Rings -- Group Identities on Symmetric Units -- Lie Identities on Symmetric Elements -- Nilpotence of and.This book presents the results for arbitrary group identities, as well as the conditions under which the unit group or the set of symmetric units satisfies several particular group identities of interest. Let FG be the group ring of a group G over a field F. Write U(FG) for the group of units of FG. It is an important problem to determine the conditions under which U(FG) satisfies a group identity. In the mid-1990s, a conjecture of Hartley was verified, namely, if U(FG) satisfies a group identity, and G is torsion, then FG satisfies a polynomial identity. Necessary and sufficient conditions for U(FG) to satisfy a group identity soon followed. Since the late 1990s, many papers have been devoted to the study of the symmetric units; that is, those units u satisfying u* = u, where * is the involution on FG defined by sending each element of G to its inverse. The conditions under which these symmetric units satisfy a group identity have now been determined.Algebra and Applications,2192-2950 ;33Group theoryAssociative ringsAssociative algebrasGroup Theory and GeneralizationsAssociative Rings and AlgebrasGroup theory.Associative rings.Associative algebras.Group Theory and Generalizations.Associative Rings and Algebras.512.4Lee Gregory T474809MiAaPQMiAaPQMiAaPQ9911047811103321Group identities on units and symmetric units of group rings247067UNINA