Geodesic
On applications of the Cayley graphs of some finite groups of exponent five
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 1, pp. 70-78

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Let $B_0(2,5)$ be the largest two–generator finite Burnside group of exponent five. It has the order $5^{34}$. We define an automorphism $\varphi$ which translates generating elements into their inverses. Let $C_{B_0(2,5)}(\varphi)$ be the centralizer of $\varphi$ in $B_0(2,5)$. It is known that $|C_{B_0(2,5)}(\varphi)|=5^{16}$. The growth functions of the centralizer are computed for some generating sets in the article. As the result we got diameters and average diameters of corresponding the Cayley graphs of $C_{B_0(2,5(\varphi)}$.
Keywords: periodic group, collection process, Hall’s polynomials, the Cayley graph, multiprocessor computer system. 
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Alexander A. Kuznetsov; Konstantin V. Safonov. On applications of the Cayley graphs of some finite groups of exponent five. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 1, pp. 70-78. http://geodesic.mathdoc.fr/item/JSFU_2018_11_1_a10/