Efficient Finite Groups Arising in the Study of Relative Asphericity Public Deposited

http://ir.library.oregonstate.edu/concern/articles/2j62s682r

Access to this item has been restricted by repository administrators at the request of the publisher until March 07, 2017.

This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Springer-Verlag Berlin Heidelberg. The final publication is available at Springer via  http://dx.doi.org/10.1007/s00209-016-1664-3

Descriptions

Attribute NameValues
Creator
Abstract or Summary
  • We study a class of two-generator two-relator groups, denoted J[subscript n](m, k), that arise in the study of relative asphericity as groups satisfying a transitional curvature condition. Particular instances of these groups occur in the literature as finite groups of intriguing orders. Here we find infinite families of non-elementary virtually free groups and of finite metabelian non-nilpotent groups, for which we determine the orders. All Mersenne primes arise as factors of the orders of the non-metacyclic groups in the class, as do all primes from other conjecturally infinite families of primes. We classify the finite groups up to isomorphism and show that our class overlaps and extends a class of groups F[superscript a,b,c] with trivalent Cayley graphs that was introduced by C.M.Campbell, H.S.M.Coxeter, and E.F.Robertson. The theory of cyclically presented groups informs our methods and we extend part of this theory (namely, on connections with polynomial resultants) to “bicyclically presented groups” that arise naturally in our analysis. As a corollary to our main results we obtain new infinite families of finite metacyclic generalized Fibonacci groups.
Resource Type
DOI
Date Available
Date Issued
Citation
  • Bogley, W. A., & Williams, G. (2016). Efficient finite groups arising in the study of relative asphericity. Mathematische Zeitschrift 284(7), pp. 507-535. doi:10.1007/s00209-016-1664-3
Series
Keyword
Rights Statement
Funding Statement (additional comments about funding)
Publisher
Peer Reviewed
Language
Replaces
Additional Information
  • description.provenance : Made available in DSpace on 2016-03-02T23:24:31Z (GMT). No. of bitstreams: 1 BogleyEfficientFiniteGroupsArisingStudyRelativeAsphericity.pdf: 294896 bytes, checksum: a5d58a6275c0cfdca0cef7933ea2327f (MD5) Previous issue date: 2016
  • description.provenance : Approved for entry into archive by Deanne Bruner(deanne.bruner@oregonstate.edu) on 2016-03-02T23:24:31Z (GMT) No. of bitstreams: 1 BogleyEfficientFiniteGroupsArisingStudyRelativeAsphericity.pdf: 294896 bytes, checksum: a5d58a6275c0cfdca0cef7933ea2327f (MD5)
  • description.provenance : Submitted by Deanne Bruner (deanne.bruner@oregonstate.edu) on 2016-03-02T23:21:49Z No. of bitstreams: 1 BogleyEfficientFiniteGroupsArisingStudyRelativeAsphericity.pdf: 294896 bytes, checksum: a5d58a6275c0cfdca0cef7933ea2327f (MD5)
  • description.provenance : Item reinstated by Deanne Bruner (deanne.bruner@oregonstate.edu) on 2016-03-07T19:07:24Z Item was in collections: Faculty Research Publications (Mathematics) (ID: 300) Open Access Articles (OSU Faculty) (ID: 619) No. of bitstreams: 1 BogleyEfficientFiniteGroupsArisingStudyRelativeAsphericity.pdf: 294896 bytes, checksum: a5d58a6275c0cfdca0cef7933ea2327f (MD5)
  • description.provenance : Item withdrawn by Deanne Bruner (deanne.bruner@oregonstate.edu) on 2016-03-07T19:03:12Z Item was in collections: Faculty Research Publications (Mathematics) (ID: 300) Open Access Articles (OSU Faculty) (ID: 619) No. of bitstreams: 1 BogleyEfficientFiniteGroupsArisingStudyRelativeAsphericity.pdf: 294896 bytes, checksum: a5d58a6275c0cfdca0cef7933ea2327f (MD5)
  • description.provenance : Approved for entry into archive by Deanne Bruner(deanne.bruner@oregonstate.edu) on 2016-03-02T23:23:12Z (GMT) No. of bitstreams: 1 BogleyEfficientFiniteGroupsArisingStudyRelativeAsphericity.pdf: 294896 bytes, checksum: a5d58a6275c0cfdca0cef7933ea2327f (MD5)

Relationships

Parents:

This work has no parents.

Last modified

Downloadable Content

Download PDF

Items