6533b828fe1ef96bd1287c35
RESEARCH PRODUCT
Group identities on symmetric units
Antonino GiambrunoSudarshan K. SehgalPolcino Miliessubject
Involution (mathematics)Pure mathematicsInvolutionInfinite fieldAlgebra and Number Theory010102 general mathematicsGRUPOS ALGÉBRICOSAlternating groupGroup algebra01 natural sciences010101 applied mathematicsSettore MAT/02 - Algebragroup identity involutionSymmetric unitTorsion (algebra)Group algebraGroup identity0101 mathematicsMathematicsdescription
Abstract Let F be an infinite field of characteristic different from 2, G a group and ∗ an involution of G extended by linearity to an involution of the group algebra FG. Here we completely characterize the torsion groups G for which the ∗-symmetric units of FG satisfy a group identity. When ∗ is the classical involution induced from g → g − 1 , g ∈ G , this result was obtained in [A. Giambruno, S.K. Sehgal, A. Valenti, Symmetric units and group identities, Manuscripta Math. 96 (1998) 443–461].
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2009-10-01 | Journal of Algebra |