We introduce a new approach to the study of finite binary permutation groups and, as an application of our method, we prove Cherlin’s binary groups conjecture for groups with socle a finite alternating group, and for the C1-primitive actions of the finite classical groups. Our new approach involves the notion, defined with respect to a group action, of a “beautiful subset”. We demonstrate how the presence of such subsets can be used to show that a given action is not binary. In particular, the study of such sets will lead to a resolution of many of the remaining open cases of Cherlin’s binary groups conjecture.
Gill, N., Spiga, P. (2020). Binary permutation groups: Alternating and classical groups. AMERICAN JOURNAL OF MATHEMATICS, 142(1), 1-43 [10.1353/ajm.2020.0000].
Binary permutation groups: Alternating and classical groups
Spiga, P
2020
Abstract
We introduce a new approach to the study of finite binary permutation groups and, as an application of our method, we prove Cherlin’s binary groups conjecture for groups with socle a finite alternating group, and for the C1-primitive actions of the finite classical groups. Our new approach involves the notion, defined with respect to a group action, of a “beautiful subset”. We demonstrate how the presence of such subsets can be used to show that a given action is not binary. In particular, the study of such sets will lead to a resolution of many of the remaining open cases of Cherlin’s binary groups conjecture.File | Dimensione | Formato | |
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