Geodesic
The Cayley graphs of Burnside groups of exponent~$3$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 248-254

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Let $B_k=B(k,3)$ be the $k$-generator Burnside group of exponent $3$. Previously unknown Hall’s polynomials of $B_k$ for $k\leq 4$ are calculated. For $k>4$ polynomials are calculated similarly but their output takes considerably more space. Then using computer calculations for $2\leq k\leq 4$ were obtained diameters and average diameters of the Cayley graphs of $ B_k $ and their some factors generated by the symmetric generating sets. It is shown that these graphs have better characteristics than hypercubes. It can be concluded that the Cayley graphs of $ B_k $ deserve attention in the design of advanced topologies of multiprocessor computer systems.
Keywords: periodic group, collection process, Hall’s polynomials, the Cayley graph, multiprocessor computer system. 
@article{SEMR_2015_12_a9,
     author = {A. A. Kuznetsov},
     title = {The {Cayley} graphs of {Burnside} groups of exponent~$3$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {248--254},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a9/}
}
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A. A. Kuznetsov. The Cayley graphs of Burnside groups of exponent~$3$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 248-254. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a9/