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Unsolved problem in mathematics:
Which finite groups are BI-groups?
Babai's problem is a problem in algebraic graph theory first proposed in 1979 by László Babai.
Babai's problem.
Let formula_1 be a finite group, let formula_2 be the set of all irreducible characters of formula_1, let formula_4 be the Cayley graph (or directed Cayley graph) corresponding to a generating subset formula_5 of formula_6, and let formula_7 be a positive integer. Is the set 
 formula_8 
an "invariant" of the graph formula_9? In other words, does formula_10 imply that formula_11? 
BI-group.
A finite group formula_1 is called a BI-group (Babai Invariant group) if formula_13 for some inverse closed subsets formula_5 and formula_15 of formula_6 implies that formula_17 for all positive integers formula_7.
Open problem.
Which finite groups are BI-groups?
References.
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