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May 21, 2016 at 15:58 comment added Misha I think proving or disproving this is well beyond the current technique.
May 17, 2016 at 8:47 comment added YCor The condition of having a $K(G,1)$ of finite type is called "of type $F_\infty$", and also equivalent to "finitely presented of type $FP_\infty$", where $FP_\infty$ is defined homologically. Reference: Brown's book on Cohomology of groups
May 17, 2016 at 7:27 history asked Timm von Puttkamer CC BY-SA 3.0