Cubic graphical regular representations of $PSL_2(q)$
Binzhou Xia, Teng Fang
TL;DR
This paper investigates the existence of cubic graphical regular representations of the finite simple groups PSL_2(q), establishing that they exist only for certain q values and require specific generating sets.
Contribution
The paper proves that cubic graphical regular representations of PSL_2(q) exist only when q is not 7 and the generating set consists of three involutions.
Findings
Existence of cubic GRRs for PSL_2(q) if and only if q ≠ 7.
Generating set must consist of three involutions.
Cubic GRRs do not exist for PSL_2(7).
Abstract
We study cubic graphical regular representations of the finite simple groups . It is shown that such graphical regular representations exist if and only if , and the generating set must consist of three involutions.
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Taxonomy
TopicsFinite Group Theory Research · Algebraic structures and combinatorial models · Advanced Algebra and Geometry