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Volumn 108, Issue 1, 2004, Pages 193-204

Finite automata of polynomial growth do not generate a free group

Author keywords

automorphisms of trees; finite automata; free groups; polynomial growth; rooted tree

Indexed keywords


EID: 10044284507     PISSN: 00465755     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10711-004-2368-0     Document Type: Article
Times cited : (27)

References (10)
  • 1
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    • Brunner, A. and Sidki, S.: The generation of GL(n, ℤ) by finite-state automata, Internat. J. Algebra Comput. 8 (1998), 127-139.
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    • Brunner, A.1    Sidki, S.2
  • 2
    • 15744369362 scopus 로고    scopus 로고
    • Automorphisms of the binary tree: State-closed subgroups and dynamics of 1/2-endomorphisms
    • T. M. Müller (ed.), Cambridge University Press
    • Nekrachevych, V. V. and Sidki, S.: Automorphisms of the binary tree: state-closed subgroups and dynamics of 1/2-endomorphisms, In: T. M. Müller (ed.), Groups-Topological, Combinatorial and Arithmetic Aspects, Cambridge University Press, 2003.
    • (2003) Groups-Topological, Combinatorial and Arithmetic Aspects
    • Nekrachevych, V.V.1    Sidki, S.2
  • 3
    • 0000562131 scopus 로고    scopus 로고
    • Automorphisms of one-rooted trees: Growth, circuit structure and acyclicity
    • Sidki, S.: Automorphisms of one-rooted trees: growth, circuit structure and acyclicity, J. Math. Sci. 100 (2000), 1925-1943.
    • (2000) J. Math. Sci. , vol.100 , pp. 1925-1943
    • Sidki, S.1
  • 4
    • 33646940707 scopus 로고
    • On the use of graphs for calculating the basis, growth and Hilbert series of associative algebras
    • Ufnarovski, V. A.: On the use of graphs for calculating the basis, growth and Hilbert series of associative algebras, Math. USSR-Sb. 68 (1991), 417-428.
    • (1991) Math. USSR-Sb. , vol.68 , pp. 417-428
    • Ufnarovski, V.A.1
  • 5
    • 84862481921 scopus 로고    scopus 로고
    • A family of just-nonsolvable torsion-free groups defined on n-ary trees
    • Atas da XVI Escola de Álgebra, Brasília
    • Sidki, S. and Silva, E. F.: A family of just-nonsolvable torsion-free groups defined on n-ary trees, In: Atas da XVI Escola de Álgebra, Brasília, Matemática Contemporânea 21 (2001), 255-274.
    • (2001) Matemática Contemporânea , vol.21 , pp. 255-274
    • Sidki, S.1    Silva, E.F.2
  • 6
    • 0032623056 scopus 로고    scopus 로고
    • A just-nonsolvable torsion-free group defined on the binary tree
    • Brunner, A., Sidki, S. and Vieira, A. C.: A just-nonsolvable torsion-free group defined on the binary tree, J. Algebra 211 (1999), 99-114.
    • (1999) J. Algebra , vol.211 , pp. 99-114
    • Brunner, A.1    Sidki, S.2    Vieira, A.C.3
  • 7
    • 0002877636 scopus 로고
    • On the Burnside problem on periodic groups
    • Grigorchuk, R. I.: On the Burnside problem on periodic groups, Funct. Anal. Appl. 14 (1980), 41-43.
    • (1980) Funct. Anal. Appl. , vol.14 , pp. 41-43
    • Grigorchuk, R.I.1
  • 8
    • 0000775074 scopus 로고
    • On the Burnside problem on periodic groups
    • Gupta, N. and Sidki, S.: On the Burnside problem on periodic groups. Math. Z. 182 (1983), 385-388.
    • (1983) Math. Z. , vol.182 , pp. 385-388
    • Gupta, N.1    Sidki, S.2
  • 9
    • 0036874604 scopus 로고    scopus 로고
    • Wreath operations in the group of automorphisms of the binary tree
    • Brunner, A. and Sidki, S.: Wreath operations in the group of automorphisms of the binary tree, J. Algebra 257 (2002), 51-64.
    • (2002) J. Algebra , vol.257 , pp. 51-64
    • Brunner, A.1    Sidki, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.