Abstract
Using tools from algebraic graph theory, we prove that for every odd prime p there is just one proper loop of order 2p such that the automorphism group of the corresponding rank 5 association scheme contains a regular subgroup of order 4p2. Although our results were initially obtained on the basis of theoretical generalization of a tremendous number of computer algebra experiments, our final computer-free proof uses quite elementary arguments from group theory and combinatorics. In this paper we provide this computer-free proof, as well as discuss further suggested use of our methods.
Original language | English |
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Pages (from-to) | 253-276 |
Number of pages | 24 |
Journal | Beitrage zur Algebra und Geometrie |
Volume | 55 |
Issue number | 1 |
DOIs | |
State | Published - 1 Mar 2014 |
Keywords
- 3-net
- 4-vertex condition
- Association scheme
- Cayley graph
- Finite permutation group
- G-loop
- Highly symmetrical loop
- Intercalate
- Loop
- Partial difference set
- Primitive S-ring
- Strongly regular graph
- Translation loop
- Transversal design
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology