메뉴 건너뛰기




Volumn 18, Issue 8, 2008, Pages 1321-1344

A nilpotent quotient algorithm for certain infinitely presented groups and its applications

Author keywords

Lower central series; Nilpotent groups; Nilpotent quotients; Self similar groups

Indexed keywords


EID: 58149359425     PISSN: 02181967     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218196708004871     Document Type: Article
Times cited : (15)

References (35)
  • 1
    • 0242425107 scopus 로고    scopus 로고
    • Endomorphic presentations of branch groups
    • L. Bartholdi, Endomorphic presentations of branch groups, J. Algebra 268(2) (2003) 419-443.
    • (2003) J. Algebra , vol.268 , Issue.2 , pp. 419-443
    • Bartholdi, L.1
  • 2
    • 58149330940 scopus 로고    scopus 로고
    • The 2-dimension series of the just-nonsolvable BSV group
    • L. Bartholdi, The 2-dimension series of the just-nonsolvable BSV group. New Zealand J. Math. 33(1) (2004) 17-23.
    • (2004) New Zealand J. Math , vol.33 , Issue.1 , pp. 17-23
    • Bartholdi, L.1
  • 3
    • 18844410779 scopus 로고    scopus 로고
    • Lie algebras and growth in branch groups
    • L. Bartholdi, Lie algebras and growth in branch groups, Pacific J. Math. 218(2) (2005) 241-282.
    • (2005) Pacific J. Math , vol.218 , Issue.2 , pp. 241-282
    • Bartholdi, L.1
  • 4
    • 58149355216 scopus 로고    scopus 로고
    • L. Bartholdi, FR - Functionally recursive groups (2007) [A submitted GAP 4 package, see [14]].
    • L. Bartholdi, FR - Functionally recursive groups (2007) [A submitted GAP 4 package, see [14]].
  • 5
    • 0007119220 scopus 로고    scopus 로고
    • Lie methods in growth of groups and groups of finite width
    • Computational and Geometric Aspects of Modern Algebra Edinburgh, 1998, Cambridge University Press, Cambridge
    • L. Bartholdi and R. I. Grigorchuk, Lie methods in growth of groups and groups of finite width, in Computational and Geometric Aspects of Modern Algebra (Edinburgh, 1998), London Mathematical Society Lecture Note Series, Vol. 275 (Cambridge University Press, Cambridge, 2000), pp. 1-27.
    • (2000) London Mathematical Society Lecture Note Series , vol.275 , pp. 1-27
    • Bartholdi, L.1    Grigorchuk, R.I.2
  • 6
    • 0242396640 scopus 로고    scopus 로고
    • On parabolic subgroups and Hecke algebras of some fractal groups
    • L. Bartholdi and R. I. Grigorchuk, On parabolic subgroups and Hecke algebras of some fractal groups, Serdica Math. J. 28(1) (2002) 47-90.
    • (2002) Serdica Math. J , vol.28 , Issue.1 , pp. 47-90
    • Bartholdi, L.1    Grigorchuk, R.I.2
  • 7
    • 58149359542 scopus 로고    scopus 로고
    • Iterated monodromy groups of quadratic polynomials, I
    • L. Bartholdi and V. V. Nekrashevych, Iterated monodromy groups of quadratic polynomials, I, Groups Geom. Dyn. 2(3) (2008) 309-336.
    • (2008) Groups Geom. Dyn , vol.2 , Issue.3 , pp. 309-336
    • Bartholdi, L.1    Nekrashevych, V.V.2
  • 8
    • 28444453688 scopus 로고    scopus 로고
    • Amenability via random walks
    • L. Bartholdi and B. Virág, Amenability via random walks, Duke Math. J. 130(1) (2005) 39-56.
    • (2005) Duke Math. J , vol.130 , Issue.1 , pp. 39-56
    • Bartholdi, L.1    Virág, B.2
  • 9
    • 84976150852 scopus 로고
    • Wreath products and p-groups
    • G. Baumslag, Wreath products and p-groups, Proc. Cambridge Philos. Soc. 55 (1959) 224-231.
    • (1959) Proc. Cambridge Philos. Soc , vol.55 , pp. 224-231
    • Baumslag, G.1
  • 10
    • 84959600423 scopus 로고
    • A finitely generated, infinitely related group with trivial multiplicator
    • G. Baumslag, A finitely generated, infinitely related group with trivial multiplicator, Bull. Austral. Math. Soc. 5 (1971) 131-136.
    • (1971) Bull. Austral. Math. Soc , vol.5 , pp. 131-136
    • Baumslag, G.1
  • 11
    • 0032623056 scopus 로고    scopus 로고
    • A just nonsolvable torsion-free group denned on the binary tree
    • A. M. Brunner, S. Sidki and A. C. Vieira, A just nonsolvable torsion-free group denned on the binary tree, J. Algebra 211(1) (1999) 99-114.
    • (1999) J. Algebra , vol.211 , Issue.1 , pp. 99-114
    • Brunner, A.M.1    Sidki, S.2    Vieira, A.C.3
  • 12
    • 30744473897 scopus 로고
    • On groups with sub-exponential growth functions
    • J. Fabrykowski and N. Gupta, On groups with sub-exponential growth functions, J. Indian Math. Soc. (N.S.) 49(3-4) (1985) (1987) 249-256.
    • (1985) J. Indian Math. Soc. (N.S.) , vol.49 , Issue.3-4 , pp. 249-256
    • Fabrykowski, J.1    Gupta, N.2
  • 13
    • 0041048575 scopus 로고
    • On groups with sub-exponential growth functions. II
    • J. Fabrykowski and N. Gupta, On groups with sub-exponential growth functions. II, J. Indian Math. Soc. (N.S.) 56(1-4) (1991) 217-228.
    • (1991) J. Indian Math. Soc. (N.S.) , vol.56 , Issue.1-4 , pp. 217-228
    • Fabrykowski, J.1    Gupta, N.2
  • 14
    • 58149330932 scopus 로고    scopus 로고
    • The GAP Group, GAP, Groups. Algorithms, and Programming. Version 4.4.10 2007
    • The GAP Group, GAP - Groups. Algorithms, and Programming. Version 4.4.10 (2007).
  • 15
    • 0002877634 scopus 로고
    • On Burnside's problem on periodic groups
    • R. I. Grigorchuk, On Burnside's problem on periodic groups, Funktional. Anal, i Prilozhen. 14(1) (1980) 53-54.
    • (1980) Funktional. Anal, i Prilozhen , vol.14 , Issue.1 , pp. 53-54
    • Grigorchuk, R.I.1
  • 16
    • 1642540895 scopus 로고    scopus 로고
    • On the system of defining relations and the Schur multiplier of periodic groups generated by finite automata
    • Groups St. Andrews 1997 in Bath. I, Cambridge University Press, Cambridge
    • R. I. Grigorchuk, On the system of defining relations and the Schur multiplier of periodic groups generated by finite automata, in Groups St. Andrews 1997 in Bath. I, London Mathematical Society Lecture Note Series, Vol. 260 (Cambridge University Press, Cambridge, 1999), pp. 290-317.
    • (1999) London Mathematical Society Lecture Note Series , vol.260 , pp. 290-317
    • Grigorchuk, R.I.1
  • 18
    • 0036016737 scopus 로고    scopus 로고
    • R. I. Grigorchuk and A. Żuk, On a torsion-free weakly branch group defined by a three state automaton, Int. J. Algebra Comput, 12(1-2) (2002) 223-246 [International Conference on Geometric and Combinatorial Methods in Group Theory and Semigroup Theory (Lincoln, NE, 2000)].
    • R. I. Grigorchuk and A. Żuk, On a torsion-free weakly branch group defined by a three state automaton, Int. J. Algebra Comput, 12(1-2) (2002) 223-246 [International Conference on Geometric and Combinatorial Methods in Group Theory and Semigroup Theory (Lincoln, NE, 2000)].
  • 19
    • 58149333963 scopus 로고    scopus 로고
    • R. I. Grigorchuk and A. Żuk, Spectral properties of a torsion-free weakly branch group defined by a three state automaton, in Computational and Statistical Group Theory (Las Vegas. NV/Hoboken, NJ, 2001), Contemporary Mathematics, 298 (American Mathematical Society, Providence, R.I, 2002), pp. 57-82.
    • R. I. Grigorchuk and A. Żuk, Spectral properties of a torsion-free weakly branch group defined by a three state automaton, in Computational and Statistical Group Theory (Las Vegas. NV/Hoboken, NJ, 2001), Contemporary Mathematics, Vol. 298 (American Mathematical Society, Providence, R.I, 2002), pp. 57-82.
  • 20
    • 0000775074 scopus 로고
    • On the Burnside problem for periodic groups
    • N. Gupta and S. Sidki, On the Burnside problem for periodic groups, Math. Z. 182(3) (1983) 385-388.
    • (1983) Math. Z , vol.182 , Issue.3 , pp. 385-388
    • Gupta, N.1    Sidki, S.2
  • 21
    • 0346861727 scopus 로고
    • Some infinite p-groups
    • N. Gupta and S. Sidki, Some infinite p-groups, Algebra i Logika 22(5) (1983) 584-589.
    • (1983) Algebra i Logika , vol.22 , Issue.5 , pp. 584-589
    • Gupta, N.1    Sidki, S.2
  • 22
    • 58149333970 scopus 로고    scopus 로고
    • R. Hartung, NQL - Nilpotent quotients of L-presented groups (2007) [A submitted GAP 4 package, see [14]].
    • R. Hartung, NQL - Nilpotent quotients of L-presented groups (2007) [A submitted GAP 4 package, see [14]].
  • 26
    • 0347041030 scopus 로고
    • Concerning nilpotent wreath products
    • H. Liebeck, Concerning nilpotent wreath products, Proc. Cambridge Philos. Soc. 58 (1962) 443-451.
    • (1962) Proc. Cambridge Philos. Soc , vol.58 , pp. 443-451
    • Liebeck, H.1
  • 27
    • 0001443098 scopus 로고
    • A set of defining relations for the Grigorchuk group
    • 634
    • I. G. Lysënok, A set of defining relations for the Grigorchuk group, Mat. Zametki 38(4) (1985) 503-516 634.
    • (1985) Mat. Zametki , vol.38 , Issue.4 , pp. 503-516
    • Lysënok, I.G.1
  • 29
    • 58149344069 scopus 로고    scopus 로고
    • W. Nickel, Computing nilpotent quotients of finitely presented groups, in Geometric and Computational Perspectives on Infinite Groups (Minneapolis, MN and New Brunswick, NJ, 1994), DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 25 (American Mathematical Society, Providence, R.I, 1996), pp. 175-191.
    • W. Nickel, Computing nilpotent quotients of finitely presented groups, in Geometric and Computational Perspectives on Infinite Groups (Minneapolis, MN and New Brunswick, NJ, 1994), DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 25 (American Mathematical Society, Providence, R.I, 1996), pp. 175-191.
  • 30
    • 58149327565 scopus 로고    scopus 로고
    • W. Nickel, NQ - Nilpotent quotients of finitely presented groups (1998) [A refereed GAP 4 package, see [14]].
    • W. Nickel, NQ - Nilpotent quotients of finitely presented groups (1998) [A refereed GAP 4 package, see [14]].
  • 32
    • 0007685993 scopus 로고    scopus 로고
    • Lower central series of a, group of tree automorphisms
    • 319
    • A. V. Rozhkov, Lower central series of a, group of tree automorphisms, Mat. Zametki 60(2) (1996) 225-237 319.
    • (1996) Mat. Zametki , vol.60 , Issue.2 , pp. 225-237
    • Rozhkov, A.V.1
  • 33
    • 33751077855 scopus 로고
    • The lower central order of a wreath product of finite abelian groups
    • K. S. Seksenbaev, The lower central order of a wreath product of finite abelian groups, Vestnik Akad. Nauk Kazakh. SSR (3) (1978) 77-78.
    • (1978) Vestnik Akad. Nauk Kazakh. SSR , vol.3 , pp. 77-78
    • Seksenbaev, K.S.1
  • 34
    • 0002782677 scopus 로고
    • The presentation problem
    • On a 2-generated infinite 3-group
    • S. Sidki, On a 2-generated infinite 3-group: The presentation problem, J. Algebra 110(1) (1987) 13-23.
    • (1987) J. Algebra , vol.110 , Issue.1 , pp. 13-23
    • Sidki, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.