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Sibirskii Matematicheskii Zhurnal, 2019, Volume 60, Number 2, Pages 360–375
DOI: https://doi.org/10.33048/smzh.2019.60.208
(Mi smj3080)
 

This article is cited in 6 scientific papers (total in 6 papers)

The $2$-closure of a $\frac32$-transitive group in polynomial time

A. V. Vasil'evab, D. V. Churikovab

a Novosibirsk State University, Novosibirsk, Russia
b Sobolev Institute of Mathematics, Novosibirsk, Russia
Full-text PDF (362 kB) Citations (6)
References:
Abstract: Let $G$ be a permutation group on a finite set $\Omega$. The $k$-closure $G^{(k)}$ of $G$ is the largest subgroup of the symmetric group $\mathrm{Sym}\,(\Omega)$ having the same orbits with $G$ on the $k$th Cartesian power $\Omega^k$ of $\Omega$. The group $G$ is called $\frac32$-transitive, if $G$ is transitive and the orbits of a point stabilizer $G_a$ on $\Omega\{a\}$ are of the same size greater than $1$. We prove that the $2$-closure $G^{(2)}$ of a $\frac32$-transitive permutation group $G$ can be found in polynomial time in size of $\Omega$. Moreover, if the group $G$ is not $2$-transitive, then for every positive integer $k$ its $k$-closure can be found within the same time. Applying the result, we prove the existence of a polynomial-time algorithm for solving the isomorphism problem for schurian $\frac32$-homogeneous coherent configurations, that is coherent configurations naturally associated with $\frac32$-transitive groups.
Keywords: $k$-closure of a permutation group, $\frac32$-transitive group, $\frac32$-homogeneous coherent configuration, schurian coherent configuration, isomorphism of coherent configurations.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00752_а
The authors were supported by the Russian Foundation for Basic Research (Grant 18-01-00752).
Received: 01.10.2018
Revised: 15.11.2018
Accepted: 19.12.2018
English version:
Siberian Mathematical Journal, 2019, Volume 60, Issue 2, Pages 279–290
DOI: https://doi.org/10.1134/S0037446619020083
Bibliographic databases:
Document Type: Article
UDC: 512.542.7
Language: Russian
Citation: A. V. Vasil'ev, D. V. Churikov, “The $2$-closure of a $\frac32$-transitive group in polynomial time”, Sibirsk. Mat. Zh., 60:2 (2019), 360–375; Siberian Math. J., 60:2 (2019), 279–290
Citation in format AMSBIB
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\paper The $2$-closure of a $\frac32$-transitive group in polynomial time
\jour Sibirsk. Mat. Zh.
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\pages 360--375
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  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Сибирский математический журнал Siberian Mathematical Journal
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