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On the Asphericity of Length Five Relative Group Presentations
Author(s) -
Howie J.,
Metaftsis V.
Publication year - 2001
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611500012752
Subject(s) - mathematics , group (periodic table) , presentation (obstetrics) , mathematics subject classification , combinatorics , subject (documents) , physics , computer science , medicine , library science , quantum mechanics , radiology
We investigate asphericity of the relative group presentation 〈 G,t ∣atbtctdtet=1〉 and prove it aspherical provided thesubgroup of G generated by ab −1 , bc −1 , cd −1 , de −1 is neither finite cyclic nor a finite triangle group. We also prove a similar result for the closely related relative group presentation 〈 G,s,t ∣ αsβsγt=1=δtεtζs −1 〉. 2000 Mathematics Subject Classification : 20F05, 57M05.