Vikraman Arvind, Jacobo Toran

The Group Isomorphism problem consists in deciding whether two input

groups $G_1$ and $G_2$ given by their multiplication tables are

isomorphic. We first give a 2-round Arthur-Merlin protocol for the

Group Non-Isomorphism problem such that on input groups $(G_1,G_2)$

of size $n$, Arthur uses ...
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Fabian Wagner

The group isomorphism problem consists in deciding whether two groups $G$ and $H$

given by their multiplication tables are isomorphic.

An algorithm for group isomorphism attributed to Tarjan runs in time $n^{\log n + O(1)}$, c.f. [Mil78].

Miller and Monk showed in [Mil79] that group isomorphism can be many-one ... more >>>

Joshua Grochow, Youming Qiao

The isomorphism problem for groups given by multiplication tables (GpI) is well-known to be solvable in n^O(log n) time, but only recently has there been significant progress towards polynomial time. For example, in 2012 Babai et al. (ICALP 2012) gave a polynomial-time algorithm for groups with no abelian normal subgroups. ... more >>>