Matches in SemOpenAlex for { <https://semopenalex.org/work/W2040384619> ?p ?o ?g. }
Showing items 1 to 100 of
100
with 100 items per page.
- W2040384619 endingPage "275" @default.
- W2040384619 startingPage "275" @default.
- W2040384619 abstract "It is an essential principle employed in this paper that properties of a group which has only a multiplication can be studied in a ring which has both additive and multiplicative operations. We also achieve, to a certain extent, a unified theory to explain some facts concerning finitely generated groups which are contained in the works of J. W. Alexander, W. Magnus, K. Reidemeister, and R. H. Fox. A group may be defined by generators and relations; i.e., it may be taken as a factor group F/R, where R is a normal subgroup of a free group F. H. Hopf [5] has shown that [F, F]/[F, R] is invariantly defined for F/R; to be explicit, F/R-F'/R' implies [F, F]/[F, R]-[F', F']/[F', R']. After some preliminaries about group rings in ?1, we proceed to establish a theory of presentations of groups and to generalize the above mentioned factor group in ?3. A family of invariantly defined quotient rings are obtained from the group ring of JF of F over J. In ?5, we extract invariants from these quotient rings by mapping each of them homomorphically into another ring of a suitable structure. The homomorphisms we use for this purpose are those induced by a homomorphism of JF into a noncommutative formal power series ring due to Magnus. A family of groups under our consideration for equivalence by isomorphism often have some common properties. For example, in the family of knot groups, each group made abelian is infinite cyclic. Therefore stronger invariants may be expected. Having this in mind, we develop the B-presentation theory in ?6. In order to derive invariants from the invariantly defined quotient rings just mentioned, Fox free differentiation becomes our main tool. Invariants resembling Alexander polynomials are produced; the computation for these invariants bears close relation with the Jacobian matrix theory in [4 ]. ?4 is mainly concerned with properties of noncommutative formal power series rings. The following notations will be universal in this paper: For elements u1, u2, of a group, [u1, u2] =ulu2u' 1uj, and [u1, * * , uP1]= [[u1, * u, up], up+i], p>2. Let A and B be subgroups of" @default.
- W2040384619 created "2016-06-24" @default.
- W2040384619 creator A5047423559 @default.
- W2040384619 date "1954-02-01" @default.
- W2040384619 modified "2023-09-26" @default.
- W2040384619 title "A group ring method for finitely generated groups" @default.
- W2040384619 cites W157718562 @default.
- W2040384619 cites W1966778897 @default.
- W2040384619 cites W1977466673 @default.
- W2040384619 cites W1996454832 @default.
- W2040384619 cites W2080955166 @default.
- W2040384619 cites W2087000236 @default.
- W2040384619 cites W2128333270 @default.
- W2040384619 cites W2146450174 @default.
- W2040384619 cites W2313637748 @default.
- W2040384619 doi "https://doi.org/10.1090/s0002-9947-1954-0060510-2" @default.
- W2040384619 hasPublicationYear "1954" @default.
- W2040384619 type Work @default.
- W2040384619 sameAs 2040384619 @default.
- W2040384619 citedByCount "4" @default.
- W2040384619 crossrefType "journal-article" @default.
- W2040384619 hasAuthorship W2040384619A5047423559 @default.
- W2040384619 hasBestOaLocation W20403846191 @default.
- W2040384619 hasConcept C105515060 @default.
- W2040384619 hasConcept C114614502 @default.
- W2040384619 hasConcept C115624301 @default.
- W2040384619 hasConcept C118615104 @default.
- W2040384619 hasConcept C134306372 @default.
- W2040384619 hasConcept C136170076 @default.
- W2040384619 hasConcept C162860070 @default.
- W2040384619 hasConcept C178790620 @default.
- W2040384619 hasConcept C185592680 @default.
- W2040384619 hasConcept C199422724 @default.
- W2040384619 hasConcept C202444582 @default.
- W2040384619 hasConcept C203436722 @default.
- W2040384619 hasConcept C20725272 @default.
- W2040384619 hasConcept C2780378348 @default.
- W2040384619 hasConcept C2781311116 @default.
- W2040384619 hasConcept C33923547 @default.
- W2040384619 hasConcept C4042151 @default.
- W2040384619 hasConcept C42747912 @default.
- W2040384619 hasConcept C68797384 @default.
- W2040384619 hasConcept C76572486 @default.
- W2040384619 hasConcept C8010536 @default.
- W2040384619 hasConcept C92788228 @default.
- W2040384619 hasConcept C95627345 @default.
- W2040384619 hasConceptScore W2040384619C105515060 @default.
- W2040384619 hasConceptScore W2040384619C114614502 @default.
- W2040384619 hasConceptScore W2040384619C115624301 @default.
- W2040384619 hasConceptScore W2040384619C118615104 @default.
- W2040384619 hasConceptScore W2040384619C134306372 @default.
- W2040384619 hasConceptScore W2040384619C136170076 @default.
- W2040384619 hasConceptScore W2040384619C162860070 @default.
- W2040384619 hasConceptScore W2040384619C178790620 @default.
- W2040384619 hasConceptScore W2040384619C185592680 @default.
- W2040384619 hasConceptScore W2040384619C199422724 @default.
- W2040384619 hasConceptScore W2040384619C202444582 @default.
- W2040384619 hasConceptScore W2040384619C203436722 @default.
- W2040384619 hasConceptScore W2040384619C20725272 @default.
- W2040384619 hasConceptScore W2040384619C2780378348 @default.
- W2040384619 hasConceptScore W2040384619C2781311116 @default.
- W2040384619 hasConceptScore W2040384619C33923547 @default.
- W2040384619 hasConceptScore W2040384619C4042151 @default.
- W2040384619 hasConceptScore W2040384619C42747912 @default.
- W2040384619 hasConceptScore W2040384619C68797384 @default.
- W2040384619 hasConceptScore W2040384619C76572486 @default.
- W2040384619 hasConceptScore W2040384619C8010536 @default.
- W2040384619 hasConceptScore W2040384619C92788228 @default.
- W2040384619 hasConceptScore W2040384619C95627345 @default.
- W2040384619 hasIssue "2" @default.
- W2040384619 hasLocation W20403846191 @default.
- W2040384619 hasOpenAccess W2040384619 @default.
- W2040384619 hasPrimaryLocation W20403846191 @default.
- W2040384619 hasRelatedWork W1505089509 @default.
- W2040384619 hasRelatedWork W1628075280 @default.
- W2040384619 hasRelatedWork W1975977663 @default.
- W2040384619 hasRelatedWork W1989041020 @default.
- W2040384619 hasRelatedWork W2011633960 @default.
- W2040384619 hasRelatedWork W2050944259 @default.
- W2040384619 hasRelatedWork W2105283037 @default.
- W2040384619 hasRelatedWork W2169046041 @default.
- W2040384619 hasRelatedWork W2298345843 @default.
- W2040384619 hasRelatedWork W2315357942 @default.
- W2040384619 hasRelatedWork W2320643507 @default.
- W2040384619 hasRelatedWork W2338681715 @default.
- W2040384619 hasRelatedWork W2355129260 @default.
- W2040384619 hasRelatedWork W2475183585 @default.
- W2040384619 hasRelatedWork W2963602331 @default.
- W2040384619 hasRelatedWork W2997591368 @default.
- W2040384619 hasRelatedWork W3120664276 @default.
- W2040384619 hasRelatedWork W3135416334 @default.
- W2040384619 hasRelatedWork W3147037213 @default.
- W2040384619 hasRelatedWork W2039132914 @default.
- W2040384619 hasVolume "76" @default.
- W2040384619 isParatext "false" @default.
- W2040384619 isRetracted "false" @default.
- W2040384619 magId "2040384619" @default.
- W2040384619 workType "article" @default.