Timeline for Embedding in f.p. simple groups
Current License: CC BY-SA 3.0
4 events
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| Mar 12, 2015 at 17:39 | comment | added | MCC | @Victor: This is not true; the Higman Embedding Theorem is very constructive. Given a recursive presentation (finite set of generators, and Turing machine T which enumerates relators), you can explicitly construct a finitely presented group into which it embeds, as well as an explicit embedding. The number of generators and relators in this new group is linear in n and s (n = number of generators in original group, s = number of states of T) See J. Rotman, An introduction to the theory of groups, Springer-Verlag, New York, (1995), chapter 12. | |
| Aug 24, 2011 at 17:58 | vote | accept | Victor | ||
| Aug 24, 2011 at 17:58 | comment | added | Victor | Thanks, Derek! So, this question is really great then!! The thing about Boone-Higman Theorem is that it rests on Higman's Embedding Theorem, the proof of which is quite "non-constructive" (well, it is difficult to wait for some effective finite presentation when working with general recursively enumerable presentations), and when one tries to find a finite presentation for a simple group to embed a given presentation, there is needed some sort of "constructiveness". I guess there must be invented something completely new. | |
| Aug 24, 2011 at 16:56 | history | answered | Derek Holt | CC BY-SA 3.0 |