TY - JOUR
T1 - Testability in group theory
AU - Becker, Oren
AU - Lubotzky, Alexander
AU - Mosheiff, Jonathan
N1 - Publisher Copyright:
© 2023, The authors.
PY - 2023/9
Y1 - 2023/9
N2 - This paper is a journal counterpart to [5], in which we initiate the study of property testing problems concerning a finite system of relations E between permutations, generalizing the study of stability in permutations. To every such system E, a group Γ = ΓE is associated and the testability of E depends only on Γ (just like in Galois theory, where the solvability of a polynomial is determined by the solvability of the associated group). This leads to the notion of testable groups, and, more generally, Benjamini–Schramm rigid groups. The paper presents an ensemble of tools to check if a given group Γ is testable/BS-rigid or not.
AB - This paper is a journal counterpart to [5], in which we initiate the study of property testing problems concerning a finite system of relations E between permutations, generalizing the study of stability in permutations. To every such system E, a group Γ = ΓE is associated and the testability of E depends only on Γ (just like in Galois theory, where the solvability of a polynomial is determined by the solvability of the associated group). This leads to the notion of testable groups, and, more generally, Benjamini–Schramm rigid groups. The paper presents an ensemble of tools to check if a given group Γ is testable/BS-rigid or not.
UR - http://www.scopus.com/inward/record.url?scp=85173637791&partnerID=8YFLogxK
U2 - 10.1007/s11856-023-2503-y
DO - 10.1007/s11856-023-2503-y
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85173637791
SN - 0021-2172
VL - 256
SP - 61
EP - 90
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -