In this paper we discuss a genetic version (GWA) of Whitehead 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 algorithm in free groups of rank > 5. Experimenting with GWA we collected an interesting numerical data that clarifies the time-complexity of Whitehead’s Problem in general. ...

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. We analyze the homological behavior of the attaching maps in the 2-local Good-willie tower of the identity evaluated at S 1. We show that they exhibit the same homological behavior as the James-Hopf maps used by N. Kuhn to prove the 2-primary Whitehead conjecture. We use this t...

. Society LAlvarez, Crawford, Good, and Stevenson, Phys. Rev. 100, 1264(A} (1955)j. ' Birge, Haddock, Kerth, Peterson, Sandweiss, Stork, and Whitehead, Phys. Rev. 99, 329 (1955). ' Sirge, Haddock, Kerth, Peterson, Sandweiss, Stork, and Whitehead, University of California Radiation Laboratory Report UCRL-3031 (unpublished}; also Proceedings of the Pisa Conference on Elementary Particles, 1955 LN...

A (right R-) module N is said to be a Whitehead test module for projectivity (shortly: a p-test module) provided for each module M , ExtR(M,N) = 0 implies M is projective. Dually, i-test modules are defined. For example, Z is a p-test abelian group iff each Whitehead group is free. Our first main result says that if R is a right hereditary non-right perfect ring, then the existence of p-test mo...

Even though the (untwisted) Whitehead doubling operation kills all known abelian invariants of knots (and makes them topologically slice), we show that it does not kill the rational function that equals to the 2-loop part of the Kontsevich integral.

We show that finite-dimensional Lie algebras over a field of characteristic zero such that the second cohomology group in every finite-dimensional module vanishes, are, essentially, semisimple.

We investigate the Whiteheadness of Borel abelian groups (א1-free, without loss of generality as otherwise this is trivial). We show that CH (and even WCH) implies any such abelian group is free, and always א2-free. 1998 Mathematics Subject Classification 03C60, 03E15, 20K20.

It is proved undecidable in ZFC + GCH whether every Z-module has a {Z}-precover. Let F be a class of R-modules of the form C = {A : Ext(A,C) = 0 for all C ∈ C} for some class C. The first author and Jan Trlifaj proved [7] that a sufficient condition for every module M to have an F -precover is that there is a module B such that F = {B} (= {A : Ext(B,A) = 0}). In [8], generalizing a method used ...

In the paper ‘Automorphic functions for a Whitehead-complement group’ [5], Matsumoto, Nishi and Yoshida constructed automorphic functions on real 3–dimensional hyperbolic space for a Kleinian group called the Whitehead-link-complement group. For a Kleinian group (of the first kind), no automorphic function/form has been studied before. In this note, their motivation is presented with a historic...