In this paper we discuss several heuristic strategies which allow one to solve the Whitehead’s minimization problem much faster (on most inputs) than the classical Whitehead algorithm. The mere fact that these strategies work in practice leads to several interesting mathematical conjectures. In particular, we conjecture that the length of most non-minimal elements in a free group can be reduced...

In this note, we try to shed some light on the relationships between the Hopf invariant, Kervaire invariant, and Whitehead square. More specifically, we prove two classical results (theorems 2.1 and 3.1) in a way that seems more transparent (at least to the author) than what is found in the literature. No new results are claimed, only a different exposition. In addition to the references cited,...

cultures of lactic streptococci. J. Dairy Research, 5, 197-207. WHITEHEAD, H. R., AND COX, G. A. 1936 Bacteriophage phenomena in cultures of lactic streptococci. J. Dairy Research, 7, 55-62. WHITEHEAD, H. R., AND HUNTER, G. J. E. 1937 Observations on the activity of bacteriophage in the group of lactic streptococci. J. Path. Bacteriol., 44, 337-347. WHITEHEAD, H. R., AND HUNTER, G. J. E. 1947 B...

We give a combinatorial equivalent to the existence of a non-free hereditarily separable group of cardinality א1. This can be used, together with a known combinatorial equivalent of the existence of a non-free Whitehead group, to prove that it is consistent that every Whitehead group is free but not every hereditarily separable group is free. We also show that the fact that Z is a p.i.d. with i...