Babai's problem
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.[1]
Babai's problem
[edit]Let be a finite group, let be the set of all irreducible characters of , let be the Cayley graph (or directed Cayley graph) corresponding to a generating subset of , and let be a positive integer. Is the set
an invariant of the graph ? In other words, does imply that ?
BI-group
[edit]A finite group is called a BI-group (Babai Invariant group)[2] if for some inverse closed subsets and of implies that for all positive integers .
Open problem
[edit]Which finite groups are BI-groups?[3]
See also
[edit]References
[edit]- ^ Babai, László (October 1979), "Spectra of Cayley graphs", Journal of Combinatorial Theory, Series B, 27 (2): 180–189, doi:10.1016/0095-8956(79)90079-0
- ^ Abdollahi, Alireza; Zallaghi, Maysam (10 February 2019). "Non-Abelian finite groups whose character sums are invariant but are not Cayley isomorphism". Journal of Algebra and Its Applications. 18 (1): 1950013. arXiv:1710.04446. doi:10.1142/S0219498819500130.
- ^ Abdollahi, Alireza; Zallaghi, Maysam (24 August 2015). "Character Sums for Cayley Graphs". Communications in Algebra. 43 (12): 5159–5167. doi:10.1080/00927872.2014.967398.