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Oct 27, 2019 at 7:27 comment added YCor To complement @HJRW's comment, the original question has now been answered (by B. Steinberg below), while the accepted answer does not even address it.
Oct 27, 2019 at 0:51 answer added Benjamin Steinberg timeline score: 12
Mar 20, 2010 at 5:24 answer added anon timeline score: 2
Feb 27, 2010 at 15:57 comment added Chad Groft Perhaps. I'm still interested in the original question, but a modified form of Rice's theorem would be nice as well.
Feb 27, 2010 at 2:49 comment added HJRW At the risk of sounding churlish, I think the original question, about finiteness properties, was really interesting, and the modified version is really dull.
Feb 23, 2010 at 14:18 vote accept Chad Groft
Feb 23, 2010 at 5:10 comment added François G. Dorais (Stillwell's example shot down my earlier comment, so I deleted it.)
Feb 23, 2010 at 5:01 history edited Chad Groft CC BY-SA 2.5
Full Rice's-theorem analogue impossible
Feb 23, 2010 at 4:34 answer added John Stillwell timeline score: 12
Feb 23, 2010 at 3:28 answer added Joel David Hamkins timeline score: 3
Feb 23, 2010 at 3:17 comment added Joel David Hamkins Your revised question is truly outstanding! I had already voted up your previous question, but now all I want to know whether Rice's theorem holds for finite group presentations.
Feb 23, 2010 at 2:28 comment added HJRW Here's an example of an interesting question whose decidability status is unknown. 'Does G have a proper subgroup of finite index?'
Feb 23, 2010 at 2:21 answer added HJRW timeline score: 3
Feb 23, 2010 at 1:33 history edited Chad Groft CC BY-SA 2.5
added acknowledgement of Henry's comment and Rice's theorem
Feb 22, 2010 at 14:46 answer added Mariano Suárez-Álvarez timeline score: 9
Feb 21, 2010 at 23:26 comment added Reid Barton For my edification, can you give an example of a finitely presented group not in F_3?
Feb 21, 2010 at 3:37 history asked Chad Groft CC BY-SA 2.5