Matches in SemOpenAlex for { <https://semopenalex.org/work/W2046378510> ?p ?o ?g. }
Showing items 1 to 84 of
84
with 100 items per page.
- W2046378510 abstract "We show that G. Baumslag's growth function for the free group is not algebraic. Recently, G. Baumslag has introduced some new numerical invariants for the class fT of finitely generated residually torsion-free nilpotent groups. Recall that for n > 1 , we let yn+x(X) = [yn(X), X], yx(X) = X and this defines the lower central series of the group X . Since the group X/yn+x(X) is nilpotent it has a torsion subgroup consisting of all the elements of finite order; hence we can define the subgroup 7„(X) of X so that yn(X)/yn+x(X) is the torsion subgroup of the quotient group 7n(X)/yn+x(X). The class ?7 can then be defined to consist of those groups which satisfy M It follows easily from the definition of yn(X) and the finite generation of X that groups in this class have the property that the successive quotients yn(X)/yn+x(X) are finitely generated free Abelian groups; let the ranks of these finitely generated free Abelian groups be denoted rn(X). Let sn = ?~2k=x rk ; the lower central series dimension of X is and their growth series of X is the generating function oo Gr(X) = YdSn(X)zn. n= These invariants of X are analogs of the notion of the dimension of a variety and the Poincare series of its associated graded local algebra. One would expect then that the size of S(X), a measure of the degree of growth of the coefficients sn(X), is related to the nature of the function Gr(A'), i.e. whether Received by the editors May 31, 1989 and, in revised form, October 17, 1989. 1980 Mathematics Subject Classification (1985 Revision). Primary 20F18." @default.
- W2046378510 created "2016-06-24" @default.
- W2046378510 creator A5079818870 @default.
- W2046378510 creator A5087824158 @default.
- W2046378510 date "1990-03-01" @default.
- W2046378510 modified "2023-09-24" @default.
- W2046378510 title "Growth functions for residually torsion-free nilpotent groups" @default.
- W2046378510 cites W2795963767 @default.
- W2046378510 doi "https://doi.org/10.1090/s0002-9939-1990-1017843-x" @default.
- W2046378510 hasPublicationYear "1990" @default.
- W2046378510 type Work @default.
- W2046378510 sameAs 2046378510 @default.
- W2046378510 citedByCount "1" @default.
- W2046378510 crossrefType "journal-article" @default.
- W2046378510 hasAuthorship W2046378510A5079818870 @default.
- W2046378510 hasAuthorship W2046378510A5087824158 @default.
- W2046378510 hasBestOaLocation W20463785101 @default.
- W2046378510 hasConcept C105515060 @default.
- W2046378510 hasConcept C114614502 @default.
- W2046378510 hasConcept C136170076 @default.
- W2046378510 hasConcept C140865510 @default.
- W2046378510 hasConcept C141071460 @default.
- W2046378510 hasConcept C14669601 @default.
- W2046378510 hasConcept C162860070 @default.
- W2046378510 hasConcept C178790620 @default.
- W2046378510 hasConcept C185592680 @default.
- W2046378510 hasConcept C188440111 @default.
- W2046378510 hasConcept C199422724 @default.
- W2046378510 hasConcept C202444582 @default.
- W2046378510 hasConcept C206219070 @default.
- W2046378510 hasConcept C2781311116 @default.
- W2046378510 hasConcept C33923547 @default.
- W2046378510 hasConcept C50555996 @default.
- W2046378510 hasConcept C71924100 @default.
- W2046378510 hasConcept C77021192 @default.
- W2046378510 hasConcept C77461463 @default.
- W2046378510 hasConcept C81008192 @default.
- W2046378510 hasConceptScore W2046378510C105515060 @default.
- W2046378510 hasConceptScore W2046378510C114614502 @default.
- W2046378510 hasConceptScore W2046378510C136170076 @default.
- W2046378510 hasConceptScore W2046378510C140865510 @default.
- W2046378510 hasConceptScore W2046378510C141071460 @default.
- W2046378510 hasConceptScore W2046378510C14669601 @default.
- W2046378510 hasConceptScore W2046378510C162860070 @default.
- W2046378510 hasConceptScore W2046378510C178790620 @default.
- W2046378510 hasConceptScore W2046378510C185592680 @default.
- W2046378510 hasConceptScore W2046378510C188440111 @default.
- W2046378510 hasConceptScore W2046378510C199422724 @default.
- W2046378510 hasConceptScore W2046378510C202444582 @default.
- W2046378510 hasConceptScore W2046378510C206219070 @default.
- W2046378510 hasConceptScore W2046378510C2781311116 @default.
- W2046378510 hasConceptScore W2046378510C33923547 @default.
- W2046378510 hasConceptScore W2046378510C50555996 @default.
- W2046378510 hasConceptScore W2046378510C71924100 @default.
- W2046378510 hasConceptScore W2046378510C77021192 @default.
- W2046378510 hasConceptScore W2046378510C77461463 @default.
- W2046378510 hasConceptScore W2046378510C81008192 @default.
- W2046378510 hasLocation W20463785101 @default.
- W2046378510 hasOpenAccess W2046378510 @default.
- W2046378510 hasPrimaryLocation W20463785101 @default.
- W2046378510 hasRelatedWork W1482281234 @default.
- W2046378510 hasRelatedWork W1581119836 @default.
- W2046378510 hasRelatedWork W1965392797 @default.
- W2046378510 hasRelatedWork W1979634638 @default.
- W2046378510 hasRelatedWork W2012640668 @default.
- W2046378510 hasRelatedWork W2016526026 @default.
- W2046378510 hasRelatedWork W2025114529 @default.
- W2046378510 hasRelatedWork W2060401671 @default.
- W2046378510 hasRelatedWork W2064349455 @default.
- W2046378510 hasRelatedWork W2108841825 @default.
- W2046378510 hasRelatedWork W2113478833 @default.
- W2046378510 hasRelatedWork W2180397790 @default.
- W2046378510 hasRelatedWork W2898227362 @default.
- W2046378510 hasRelatedWork W2916301431 @default.
- W2046378510 hasRelatedWork W2953113322 @default.
- W2046378510 hasRelatedWork W2964337988 @default.
- W2046378510 hasRelatedWork W3011338801 @default.
- W2046378510 hasRelatedWork W3039641119 @default.
- W2046378510 hasRelatedWork W3098986342 @default.
- W2046378510 hasRelatedWork W3140612387 @default.
- W2046378510 isParatext "false" @default.
- W2046378510 isRetracted "false" @default.
- W2046378510 magId "2046378510" @default.
- W2046378510 workType "article" @default.