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.
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...
Since the late 1990s, many papers have examined symmetric units. This book presents results for arbitrary group identities, as well as the conditions under which the unit group or the set of symmetric units satisfies particular group identities of interest.
Since the late 1990s, many papers have examined symmetric units. This book presents results for arbitrary group identities, as well as the conditions ...
