Back to Search
Start Over
Schurity and separability of quasiregular coherent configurations.
- Source :
-
Journal of Algebra . Sep2018, Vol. 510, p180-204. 25p. - Publication Year :
- 2018
-
Abstract
- A permutation group is said to be quasiregular if each of its transitive constituents is regular, and a quasiregular coherent configuration can be thought as a combinatorial analog of such a group: the transitive constituents are replaced by the homogeneous components. In this paper, we are interested in the question when the configuration is schurian, i.e., formed by the orbitals of a permutation group, or/and separable, i.e., uniquely determined by the intersection numbers. In these terms, an old result of Hanna Neumann is, in a sense, dual to the statement that the quasiregular coherent configurations with cyclic homogeneous components are schurian. In the present paper, we (a) establish the duality in a precise form and (b) generalize the latter result by proving that a quasiregular coherent configuration is schurian and separable if the groups associated with the homogeneous components have distributive lattices of normal subgroups. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 510
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 130745010
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2018.05.027