Abstract:
In the paper the automorphism groups of regular trees are discussed. It is proved that the automorphism groups of regular trees of degree $n>2$ are complete and that the automorphism groups of regular trees of different degrees are different.
Figures: 2.
Bibliography: 5 titles.
\Bibitem{Zno77}
\by D.~V.~Znoiko
\paper The automorphism groups of regular trees
\jour Math. USSR-Sb.
\yr 1977
\vol 32
\issue 1
\pages 109--115
\mathnet{http://mi.mathnet.ru/eng/sm2802}
\crossref{https://doi.org/10.1070/SM1977v032n01ABEH002318}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=444513}
\zmath{https://zbmath.org/?q=an:0392.05031|0396.05024}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1977GE09700007}
Linking options:
https://www.mathnet.ru/eng/sm2802
https://doi.org/10.1070/SM1977v032n01ABEH002318
https://www.mathnet.ru/eng/sm/v145/i1/p124
This publication is cited in the following 7 articles:
Humberto Luiz Talpo, Marcelo Firer, “Covering number for reflections in trees”, jgth, 11:6 (2008), 869
Bartholdi L., Sidki S., “The Automorphism Tower of Groups Acting on Rooted Trees”, Trans. Am. Math. Soc., 358:1 (2006), 329–358
PIOTR W. GAWRON, VOLODYMYR V. NEKRASHEVYCH, VITALY I. SUSHCHANSKY, “CONJUGATION IN TREE AUTOMORPHISM GROUPS”, Int. J. Algebra Comput, 11:05 (2001), 529
P. Gawron, V. V. Nekrashevych, V. I. Sushchanskii, “Conjugacy classes of the automorphism group of a tree”, Math. Notes, 65:6 (1999), 787–790
John D. Dixon, Brian Mortimer, Graduate Texts in Mathematics, 163, Permutation Groups, 1996, 274
A. Lubotzky, S. Mozes, R. J. Zimmer, “Superrigidity for the commensurability group of tree lattices”, Comment Math Helv, 69:1 (1994), 523
Bass H., Lubotzky A., “Rigidity of Group-Actions on Locally Finite Trees”, Proc. London Math. Soc., 69:Part 3 (1994), 541–575