A Non‐Finitely Based Variety of Centre‐by‐Abelian‐by‐Nilpotent Groups of Exponent 8

The first example of a non‐finitely based variety of centre‐by‐abelian‐by‐nilpotent groups was found in 1995. This example has an infinite exponent but it can be seen that the method used to construct it also gives a variety that has an exponent of 128. Later it was proved that there exists a variety with similar properties but with an exponent of 32. The paper constructs a non‐finitely based variety of centre‐by‐abelian‐by‐nilpotent groups which has an exponent of 8.