The whitehead asphericity conjecture and periodic groups

Research output: Contribution to journalArticlepeer-review

Abstract

The Whitehead asphericity conjecture claims that if (A. ∥ R) is an aspherical group presentation, then for every S ⊂ R the subpresentation (A ∥ S) is also aspherical. This conjecture is generalized for presentations of groups with periodic elements by introducing almost aspherical presentations (for example, every one-relator group is almost aspherical). It is proven that the generalized Whitehead asphericity conjecture (which claims that every subpresentation of an almost aspherical presentation is also almost aspherical) is equivalent to the original Whitehead conjecture. It is also proven that the generalized Whitehead asphericity conjecture holds for Ol'shanskii's presentations of free Burnside groups of large odd exponent, presentations of Tarski monsters and others.

Original languageEnglish (US)
Pages (from-to)529-538
Number of pages10
JournalInternational Journal of Algebra and Computation
Volume9
Issue number5
DOIs
StatePublished - Jan 1 1999

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'The whitehead asphericity conjecture and periodic groups'. Together they form a unique fingerprint.

Cite this