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 J. Sib. Fed. Univ. Math. Phys., 2018, Volume 11, Issue 1, Pages 70–78 (Mi jsfu595)

On applications of the Cayley graphs of some finite groups of exponent five

Alexander A. Kuznetsov, Konstantin V. Safonov

Institute of Computer Science and Telecommunications, Reshetnev Siberian State University of Science and Technology, Krasnoyarsky Rabochy, 31, Krasnoyarsk, 660037, Russia

Abstract: 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.

 Funding Agency Grant Number Russian Foundation for Basic Research 17-47-240318_ð_à The reported study was funded by Russian Foundation for Basic Research, Government of Krasnoyarsk Territory, Krasnoyarsk Region Science and Technology Support Fund to the research project no. 17-47-240318.

DOI: https://doi.org/10.17516/1997-1397-2018-11-1-70-78

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UDC: 517.9
Accepted: 16.10.2017
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Citation: Alexander A. Kuznetsov, Konstantin V. Safonov, “On applications of the Cayley graphs of some finite groups of exponent five”, J. Sib. Fed. Univ. Math. Phys., 11:1 (2018), 70–78

Citation in format AMSBIB
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