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Algebra and Discrete Mathematics, 2016, Volume 21, Issue 2, Pages 264–281
(Mi adm567)
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This article is cited in 5 scientific papers (total in 5 papers)
RESEARCH ARTICLE
The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs
Bartłomiej Pawlik Institute of Mathematics, Silesian University of Technology, ul. Kaszubska 23, 44-100 Gliwice, Poland
Abstract:
Base (minimal generating set) of the Sylow 2-subgroup of $S_{2^n}$ is called diagonal if every element of this set acts non-trivially only on one coordinate, and different elements act on different coordinates. The Sylow 2-subgroup $P_n(2)$ of $S_{2^n}$ acts by conjugation on the set of all bases. In presented paper the stabilizer of the set of all diagonal bases in $S_n(2)$ is characterized and the orbits of the action are determined. It is shown that every orbit contains exactly $2^{n-1}$ diagonal bases and $2^{2^n-2n}$ bases at all. Recursive construction of Cayley graphs of $P_n(2)$ on diagonal bases ($n\geq2$) is proposed.
Keywords:
Sylow $p$-subgroup, group base, wreath product of groups, Cayley graphs.
Received: 10.04.2016 Revised: 30.05.2016
Citation:
Bartłomiej Pawlik, “The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs”, Algebra Discrete Math., 21:2 (2016), 264–281
Linking options:
https://www.mathnet.ru/eng/adm567 https://www.mathnet.ru/eng/adm/v21/i2/p264
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Abstract page: | 181 | Full-text PDF : | 75 | References: | 38 |
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