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This article is cited in 1 scientific paper (total in 1 paper)
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.
Received: 17.04.2017 Received in revised form: 20.04.2017 Accepted: 16.10.2017
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
Linking options:
https://www.mathnet.ru/eng/jsfu595 https://www.mathnet.ru/eng/jsfu/v11/i1/p70
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