On a finite $2,3$-generated group of period $12$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 548-556
Cet article a éte moissonné depuis la source Math-Net.Ru
Using calculations in computer algebra systems along with some theoretic results, we construct the largest finite group of period $12$ generated by an element of order $2$ and an element of order $3$. In particular, we prove that this group has order $2^{66}\cdot3^7$.
Keywords:
periodic groups, Burnside problem.
@article{SEMR_2014_11_a16,
author = {Andrei V. Zavarnitsine},
title = {On a finite $2,3$-generated group of period $12$},
journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
pages = {548--556},
year = {2014},
volume = {11},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a16/}
}
Andrei V. Zavarnitsine. On a finite $2,3$-generated group of period $12$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 548-556. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a16/
[1] D. V. Lytknia, V. D. Mazurov, A. S. Mamontov, “On local finiteness of some groups of period $12$”, Sib. Math. J., 53:6 (2012), 1105–1109 | DOI | MR
[2] V. D. Mazurov, A. S. Mamontov, “Involutions in groups of exponent $12$”, Algebra and Logic, 52:1 (2013), 67–71 | DOI | MR | Zbl
[3] A. S. Mamontov, “Groups of period $12$ without elements of order $12$”, Sib. Math. J., 54:1 (2013), 114–118 | DOI | MR | Zbl
[4] The GAP Group, GAP — Groups, Algorithms, and Programming, Version 4.6.4, , 2013 http://www.gap-system.org
[5] W. Bosma, J. Cannon, C. Playoust, “The Magma algebra system. I: The user language”, J. Symbolic Comput., 24 (1997), 235–265 | DOI | MR | Zbl