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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_р_а |
| 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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Bibliographic databases:
UDC:
517.9
Received: 17.04.2017
Received in revised form: 20.04.2017
Accepted: 16.10.2017
Language:
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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\paper On applications of the Cayley graphs of some finite groups of exponent five
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2018
\vol 11
\issue 1
\pages 70--78
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\crossref{https://doi.org/10.17516/1997-1397-2018-11-1-70-78}
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http://mi.mathnet.ru/eng/jsfu595 http://mi.mathnet.ru/eng/jsfu/v11/i1/p70
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