01 August 2015 ~ 0 Comments

A long time ago

I worked hard since my last post a year ago, mostly on isomorphism of finite groups which is a decidable problem.

Isomorphism problem is a hard problem which is known to be decidable for most groups since it is decidable for hyperbolic groups (see arXiv:1002.2590 ”The isomorphism problem for all hyperbolic groups” from François Dahmani, Vincent Guirardel). However we know large classes of groups for which this problem is undecidable like

  • free by free groups (Miller 71)
  • free abelian by free groups (Zimmermann 85)
  • solvable groups of derived length 3 (Baumslag-Gildenhuys-Strebe 85)

Even if the problem of isomorphism is decidable for finite groups (finite groups are hyperbolic), there are some interesting things to learn on this subject. This work has given me some insights on another subject I love which is: “why some theories are complete and some are not ?”


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