Search results for "Infinite field"
showing 3 items of 3 documents
Star-group identities and groups of units
2010
Analogous to *-identities in rings with involution we define *-identities in groups. Suppose that G is a torsion group with involution * and that F is an infinite field with char F ≠ 2. Extend * linearly to FG. We prove that the unit group \({\mathcal{U}}\) of FG satisfies a *-identity if and only if the symmetric elements \({\mathcal{U}^+}\) satisfy a group identity.
Group identities on symmetric units
2009
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].
Invariants of unipotent groups
1987
I’ll give a survey on the known results on finite generation of invariants for nonreductive groups, and some conjectures. You know that Hilbert’s 14th problem is solved for the invariants of reductive groups; see [12] for a survey. So the general case reduces to the case of unipotent groups. But in this case there are only a few results, some negative and some positive. I assume that k is an infinite field, say the complex numbers, but in most instances an arbitrary ring would do it.