On the Complexity of Identifying Groups without Abelian Normal Subgroups: Parallel, First Order, and GI-Hardness

Joshua A. Grochow, Dan Johnson, Michael Levet

In this paper, we exhibit an ${\text{AC}}^3$ isomorphism test for groups without Abelian normal subgroups (a.k.a. Fitting-free groups), a class for which isomorphism testing was…