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010   $a9783032046208$b(electronic bk.)
010   $z9783032046192
024 7 $a10.1007/978-3-032-04620-8
035   $a(MiAaPQ)EBC32422140
035   $a(Au-PeEL)EBL32422140
035   $a(CKB)43552486100041
035   $a(DE-He213)978-3-032-04620-8
035   $a(EXLCZ)9943552486100041
100   $a20251120d2025      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aGroup Identities on Units and Symmetric Units of Group Rings /$fby Gregory T. Lee
205   $a2nd ed. 2025.
210  1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025.
215   $a1 online resource (486 pages)
225 1 $aAlgebra and Applications,$x2192-2950 ;$v33
311 08$aPrint version: Lee, Gregory T. Group Identities on Units and Symmetric Units of Group Rings Cham : Springer London, Limited,c2025 9783032046192 
327   $aGroup Identities on Units of Group Rings -- Group Identities on Symmetric Units -- Lie Identities on Symmetric Elements -- Nilpotence of and.
330   $aThis book presents the results for arbitrary group identities, as well as the conditions under which the unit group or the set of symmetric units satisfies several particular group identities of interest. Let FG be the group ring of a group G over a field F. Write U(FG) for the group of units of FG. It is an important problem to determine the conditions under which U(FG) satisfies a group identity. In the mid-1990s, a conjecture of Hartley was verified, namely, if U(FG) satisfies a group identity, and G is torsion, then FG satisfies a polynomial identity. Necessary and sufficient conditions for U(FG) to satisfy a group identity soon followed. Since the late 1990s, many papers have been devoted to the study of the symmetric units; that is, those units u satisfying u* = u, where * is the involution on FG defined by sending each element of G to its inverse. The conditions under which these symmetric units satisfy a group identity have now been determined.
410  0$aAlgebra and Applications,$x2192-2950 ;$v33
606   $aGroup theory
606   $aAssociative rings
606   $aAssociative algebras
606   $aGroup Theory and Generalizations
606   $aAssociative Rings and Algebras
615  0$aGroup theory.
615  0$aAssociative rings.
615  0$aAssociative algebras.
615 14$aGroup Theory and Generalizations.
615 24$aAssociative Rings and Algebras.
676   $a512.4
700   $aLee$b Gregory T$0474809
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
912   $a9911047811103321
996   $aGroup identities on units and symmetric units of group rings$9247067
997   $aUNINA