In 1966, Milnor surveyed in this Bulletin [23] the concept of Whitehead torsion, focusing on the definition, topological significance and computation of Whitehead groups and their relationship to algebraic ^-theory and the congruence subgroup problem. As Milnor showed in that survey [23, Appendix 1], an affirmative solution to the congruence subgroup problem for algebraic number fields would im...

In this paper we discuss a genetic version (GWA) of the Whitehead’s algorithm, which is one of the basic algorithms in combinatorial group theory. It turns out that GWA is surprisingly fast and outperforms the standard Whitehead’s algorithm in free groups of rank ≥ 5. Experimenting with GWA we collected an interesting numerical data that clarifies the time-complexity of the Whitehead’s Problem ...