**HENRY E. HEATHERLY**

*Adjoint groups of radical rings*

**Pages** 55-68

**Received:** 2 September 1999

**Mathematics Subject Classification (2000):** 16N20

**Abstract**
Let R be a Jagacobson radical ring. This paper discusses the connections between a
ring R and its adjoint group (R, o), where a o b = a + b - ab. Both an exposition of the development of
the theory and some new results are given. Conditions on R which guarantee that (R, o) is solvable,
nilpotent, or generalized solvable are considered. A new set of conditions for a group to be isomorphic
to an adjoint group is given. Several diverse examples of Jacobson radical rings are exhibited.

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