Abstract
Let F(t) be the function field in one variable over the finite field F. We construct a surjective cellular cover γ : 𝒢 → PSL(3, F(t)), where 𝒢 = G ○ E, G = St(3, F(t)), E = Ext(ℚ/ℤ K͂2(F(t))) and G ○ E is the commuting product with G ∩ E = K͂2(F(t)). Here K͂2(F(t)) is the kernel of St(3, F(t)) ↠ PSL(3, F(t)). Since 𝒢/[𝒢, 𝒢] ≅ E/K͂2(F(t)) is a nontrivial torsion free divisible abelian group, this gives a negative answer to a question raised in the paper “Cellular covers of groups” (J. Pure and Applied Algebra 208 (2007)), by E. Farjoun, R. Göbel and the author. We asked whether a surjective cellular cover of a perfect group is perfect.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
