Code equivalence and group isomorphism

@inproceedings{Babai2011CodeEA,
  title={Code equivalence and group isomorphism},
  author={L{\'a}szl{\'o} Babai and Paolo Codenotti and Joshua A. Grochow and Youming Qiao},
  booktitle={SODA '11},
  year={2011}
}
The isomorphism problem for groups given by their multiplication tables has long been known to be solvable in time nlog n+O(1). The decades-old quest for a polynomial-time algorithm has focused on the very difficult case of class-2 nilpotent groups (groups whose quotient by their center is abelian), with little success. In this paper we consider the opposite end of the spectrum and initiate a more hopeful program to find a polynomial-time algorithm for semisimple groups, defined as groups… 
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