TY - JOUR

T1 - On symmetric units in group algebras

AU - Bovdi, Victor

N1 - Funding Information:
The research was supported by the Hungarian National Foundation for Scientific Research Grants No. T029132 and No. T025029.

PY - 2001

Y1 - 2001

N2 - Let U(KG) be the group of units of the group ring KG of the group G over a commutative ring K. The anti-automorphism g → g-1 of G can be extended linearly to an anti-automorphism a → a* of KG. Let S*(KG) = {x ∈ U(KG) | x* = x} be the set of all symmetric units of U(KG). We consider the following question: for which groups G and commutative rings K it is true that S*(KG) is a subgroup in U(KG). We answer this question when either a) G is torsion and K is a commutative G-favourable integral domain of characteristic p > 0 or b) G is non-torsion nilpotent group and KG is semiprime.

AB - Let U(KG) be the group of units of the group ring KG of the group G over a commutative ring K. The anti-automorphism g → g-1 of G can be extended linearly to an anti-automorphism a → a* of KG. Let S*(KG) = {x ∈ U(KG) | x* = x} be the set of all symmetric units of U(KG). We consider the following question: for which groups G and commutative rings K it is true that S*(KG) is a subgroup in U(KG). We answer this question when either a) G is torsion and K is a commutative G-favourable integral domain of characteristic p > 0 or b) G is non-torsion nilpotent group and KG is semiprime.

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U2 - 10.1081/AGB-100107935

DO - 10.1081/AGB-100107935

M3 - Article

AN - SCOPUS:0035567724

SN - 0092-7872

VL - 29

SP - 5411

EP - 5422

JO - Communications in Algebra

JF - Communications in Algebra

IS - 12

ER -