Free groups and involutions in the unit group of a group algebra. (Q1773927)

The authors study the existence of nonabelian free groups in the subgroup generated by the involutions of the unit group of the group algebra \(FG\) over a non-absolute field. If \(\text{char}(F)=p\neq 2\), \(G\) has no \(p\)-elements and the group of units \(U(FG)\) does not contain a nonabelian free subgroup, then the torsion part \(t(G)\) of \(G\) is an Abelian or Hamiltonian group, moreover every subgroup of \(t(G)\) is normal in \(G\). The Hamiltonian case can occur only if \(\text{char}(F)=0\).