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A non-perfect surjective cellular cover of PSL(3,F(t))
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Yoav Segev
Veröffentlicht/Copyright:
8. September 2008
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.
2000 Mathematics Subject Classification: 19C09, 55P60.
Received: 2007-04-17
Published Online: 2008-09-08
Published in Print: 2008-07-01
© Walter de Gruyter
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Artikel in diesem Heft
- A sphere theorem for a class of Reinhardt domains with constant Levi curvature
- Weighted inequalities and Stein-Weiss potentials
- Iwasawa's Local Splitting Theorem for Pro-Lie Groups
- Secondary homotopy groups
- Calderon–Zygmund type estimates for nonlinear systems with quadratic growth on the Heisenberg group
- Extensions of L∞ algebras of two even and one odd dimension
- Expander graphs and gaps between primes
- A non-perfect surjective cellular cover of PSL(3,F(t))
Artikel in diesem Heft
- A sphere theorem for a class of Reinhardt domains with constant Levi curvature
- Weighted inequalities and Stein-Weiss potentials
- Iwasawa's Local Splitting Theorem for Pro-Lie Groups
- Secondary homotopy groups
- Calderon–Zygmund type estimates for nonlinear systems with quadratic growth on the Heisenberg group
- Extensions of L∞ algebras of two even and one odd dimension
- Expander graphs and gaps between primes
- A non-perfect surjective cellular cover of PSL(3,F(t))
