On pseudofrobenius imprimitive association schemes Full article
| Journal |
Journal of Algebraic Combinatorics
ISSN: 0925-9899 , E-ISSN: 1572-9192 |
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| Output data | Year: 2023, Volume: 57, Number: 2, Pages: 385-402 Pages count : 18 DOI: 10.1007/s10801-022-01193-4 | ||||||||
| Tags | frobenius groups, permutation groups, association schemes, 05e30, 20b05, 05c60, 20c15, combinatorics, convex and discrete geometry, order, lattices, ordered algebraic structures, computer science, general, group theory and generalizations | ||||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Министерство науки и высшего образования РФ | 075-15-2019-1620 |
Abstract:
An (association) scheme is said to be Frobenius if it is the (orbital) scheme of a Frobenius group. A scheme which has the same tensor of intersection numbers as some Frobenius scheme is said to be pseudofrobenius. We establish a necessary and sufficient condition for an imprimitive pseudofrobenius scheme to be Frobenius. We also prove strong necessary conditions for existence of an imprimitive pseudofrobenius scheme which is not Frobenius. As a byproduct, we obtain a sufficient condition for an imprimitive Frobenius group G with abelian kernel to be determined up to isomorphism only by the character table of G. Finally, we prove that the Weisfeiler-Leman dimension of a circulant graph with n vertices and Frobenius automorphism group is equal to 2 unless n∈{p,p2,p3,pq,p2q} , where p and q are distinct primes.
Cite:
Ponomarenko I.
, Ryabov G.
On pseudofrobenius imprimitive association schemes
Journal of Algebraic Combinatorics. 2023. V.57. N2. P.385-402. DOI: 10.1007/s10801-022-01193-4 WOS Scopus РИНЦ OpenAlex
On pseudofrobenius imprimitive association schemes
Journal of Algebraic Combinatorics. 2023. V.57. N2. P.385-402. DOI: 10.1007/s10801-022-01193-4 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Nov 6, 2021 |
| Accepted: | Nov 19, 2022 |
| Published online: | Dec 29, 2022 |
| Published print: | Jan 31, 2024 |
Identifiers:
| Web of science: | WOS:000906936800001 |
| Scopus: | 2-s2.0-85145202547 |
| Elibrary: | 59894317 |
| OpenAlex: | W3208797046 |