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Sibirskii Matematicheskii Zhurnal, 2024, Volume 65, Number 5, Pages 808–819
DOI: https://doi.org/10.33048/smzh.2024.65.504 (Mi smj7893) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Group bijections commuting with inner automorphisms

A. N. Borodina, M. V. Neshchadimb, A. A. Simonovc

a Gorno-Altaisk State University
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
c Novosibirsk State University
Full-text PDF (272 kB) Citations (1)
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DOI: https://doi.org/10.33048/smzh.2024.65.504
Abstract: Considering the bijections of an arbitrary group $G$ onto itself which commute with all inner automorphisms, we establish the general properties. In particular, the automorphisms constitute the group $B(G)$ that includes the group of central automorphisms. Also, we fully describe $B(D_n)$ for the dihedral groups $D_n$, with $n \in {\Bbb N} \cup \{ \infty \}$.
Keywords: group, bijection, automorphism, conjugacy class, inversion, wreath product, quandle.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0009
The work was supported by the Fundamental Research Program of the Siberian Branch of the Russian Academy of Sciences (no. I.1.5, Project FWNF–2022-0009).
Received: 02.05.2024
Revised: 05.06.2024
Accepted: 20.06.2024
English version:
Siberian Mathematical Journal, 2024, Volume 65, Issue 5, Pages 1015–1025
DOI: https://doi.org/10.1134/S0037446624050045
Document Type: Article
UDC: 512.543.56
MSC: 35R30
Language: Russian
Citation: A. N. Borodin, M. V. Neshchadim, A. A. Simonov, “Group bijections commuting with inner automorphisms”, Sibirsk. Mat. Zh., 65:5 (2024), 808–819; Siberian Math. J., 65:5 (2024), 1015–1025
Citation in format AMSBIB
\Bibitem{BorNesSim24}
\by A.~N.~Borodin, M.~V.~Neshchadim, A.~A.~Simonov
\paper Group bijections commuting with inner automorphisms
\jour Sibirsk. Mat. Zh.
\yr 2024
\vol 65
\issue 5
\pages 808--819
\mathnet{http://mi.mathnet.ru/smj7893}
\transl
\jour Siberian Math. J.
\yr 2024
\vol 65
\issue 5
\pages 1015--1025
\crossref{https://doi.org/10.1134/S0037446624050045}
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