TY - JOUR
T1 - A non-perfect surjective cellular cover of PSL(3,F(t))
AU - Segev, Yoav
N1 - Funding Information:
1 Partially supported by the Israel Science Foundation grant no. 712/07.
PY - 2008/7/1
Y1 - 2008/7/1
N2 - 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 K2(F(t))) and G ○ E is the commuting product with G ∩ E = K̃2(F(t)). Here K̃2(F(t)) is the kernel of St(3, F(t)) ↠ PSL(3, F(t)). Since G/[G, G] ≅ E/K̃2(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.
AB - 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 K2(F(t))) and G ○ E is the commuting product with G ∩ E = K̃2(F(t)). Here K̃2(F(t)) is the kernel of St(3, F(t)) ↠ PSL(3, F(t)). Since G/[G, G] ≅ E/K̃2(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.
UR - http://www.scopus.com/inward/record.url?scp=51449115267&partnerID=8YFLogxK
U2 - 10.1515/FORUM.2008.036
DO - 10.1515/FORUM.2008.036
M3 - Article
AN - SCOPUS:51449115267
SN - 0933-7741
VL - 20
SP - 757
EP - 762
JO - Forum Mathematicum
JF - Forum Mathematicum
IS - 4
ER -