On circle groups of nilpotent rings of characteristic \(2\) (Q1922113)

The author proves that a nilpotent group of class 2 and exponent 4 is a circle group of a nilpotent ring of index 3 and characteristic 2. For any radical ring \(R\) one denotes the group \(R\) with multiplication \(\circ\) obtained by \(a\circ b:=a+b+ab\) for any two \(a,b\in R\) the circle group of \(R\). The question on the appearance of a nilpotent group as a circle group has applications to questions concerning the unit group of a group ring.