Matches in SemOpenAlex for { <https://semopenalex.org/work/W2323500172> ?p ?o ?g. }
Showing items 1 to 79 of
79
with 100 items per page.
- W2323500172 abstract "Mathematics is full of examples that illustrate the principle of extend and conquer. Put simply, mathematical results become clearer and more complete when the framework of the discussion is enlarged. The fundamental theorem of algebra is a good example. For it is usually difficult, if not impossible, to describe the number of integers or rational numbers that are solutions to a polynomial equation; but by enlarging the scope of the discussion to include complex numbers and by agreeing to count multiple solutions separately, we obtain the simple and elegant statement that every polynomial equation of positive degree n has exactly n complex solutions. This article discusses an example of the extend and conquer principle that arises in the representation theory of finite groupsthe Artin induction theorem. This theorem shows that every linear representation of a finite group over the field of rational numbers extends to a permutation representation of the group and, as such, provides a link between representing the elements of a finite group as linear transformations of a vector space and representing them as permutations of a set. But more importantly, when the Artin theorem is stated in terms of group characters, it provides a precise way to measure, numerically, how close the rational representations of the group are to being permutation representations. We denote this numerical measure by the symbol y. The purpose of this article is to discuss the history of y, its existence and known values, and to indicate briefly the local algebraic methods for determining this invariant." @default.
- W2323500172 created "2016-06-24" @default.
- W2323500172 creator A5078975521 @default.
- W2323500172 date "1987-11-01" @default.
- W2323500172 modified "2023-09-26" @default.
- W2323500172 title "Rational Representations of Finite Groups: The Story of γ" @default.
- W2323500172 cites W120124575 @default.
- W2323500172 cites W1964524805 @default.
- W2323500172 cites W1982884443 @default.
- W2323500172 cites W1987641735 @default.
- W2323500172 cites W2009931824 @default.
- W2323500172 cites W2035672915 @default.
- W2323500172 cites W2103648454 @default.
- W2323500172 cites W2127315534 @default.
- W2323500172 cites W601574185 @default.
- W2323500172 doi "https://doi.org/10.2307/2322816" @default.
- W2323500172 hasPublicationYear "1987" @default.
- W2323500172 type Work @default.
- W2323500172 sameAs 2323500172 @default.
- W2323500172 citedByCount "0" @default.
- W2323500172 crossrefType "journal-article" @default.
- W2323500172 hasAuthorship W2323500172A5078975521 @default.
- W2323500172 hasConcept C118615104 @default.
- W2323500172 hasConcept C121332964 @default.
- W2323500172 hasConcept C13336665 @default.
- W2323500172 hasConcept C136119220 @default.
- W2323500172 hasConcept C178790620 @default.
- W2323500172 hasConcept C185592680 @default.
- W2323500172 hasConcept C190470478 @default.
- W2323500172 hasConcept C202444582 @default.
- W2323500172 hasConcept C21308566 @default.
- W2323500172 hasConcept C24890656 @default.
- W2323500172 hasConcept C2781311116 @default.
- W2323500172 hasConcept C33923547 @default.
- W2323500172 hasConcept C37914503 @default.
- W2323500172 hasConcept C46875033 @default.
- W2323500172 hasConcept C92957085 @default.
- W2323500172 hasConceptScore W2323500172C118615104 @default.
- W2323500172 hasConceptScore W2323500172C121332964 @default.
- W2323500172 hasConceptScore W2323500172C13336665 @default.
- W2323500172 hasConceptScore W2323500172C136119220 @default.
- W2323500172 hasConceptScore W2323500172C178790620 @default.
- W2323500172 hasConceptScore W2323500172C185592680 @default.
- W2323500172 hasConceptScore W2323500172C190470478 @default.
- W2323500172 hasConceptScore W2323500172C202444582 @default.
- W2323500172 hasConceptScore W2323500172C21308566 @default.
- W2323500172 hasConceptScore W2323500172C24890656 @default.
- W2323500172 hasConceptScore W2323500172C2781311116 @default.
- W2323500172 hasConceptScore W2323500172C33923547 @default.
- W2323500172 hasConceptScore W2323500172C37914503 @default.
- W2323500172 hasConceptScore W2323500172C46875033 @default.
- W2323500172 hasConceptScore W2323500172C92957085 @default.
- W2323500172 hasLocation W23235001721 @default.
- W2323500172 hasOpenAccess W2323500172 @default.
- W2323500172 hasPrimaryLocation W23235001721 @default.
- W2323500172 hasRelatedWork W1155074308 @default.
- W2323500172 hasRelatedWork W1615580298 @default.
- W2323500172 hasRelatedWork W16782913 @default.
- W2323500172 hasRelatedWork W1972439732 @default.
- W2323500172 hasRelatedWork W2015099830 @default.
- W2323500172 hasRelatedWork W2199270623 @default.
- W2323500172 hasRelatedWork W2251300648 @default.
- W2323500172 hasRelatedWork W2465937103 @default.
- W2323500172 hasRelatedWork W2522682047 @default.
- W2323500172 hasRelatedWork W2541453503 @default.
- W2323500172 hasRelatedWork W2611102007 @default.
- W2323500172 hasRelatedWork W2756262996 @default.
- W2323500172 hasRelatedWork W2768024055 @default.
- W2323500172 hasRelatedWork W2783626036 @default.
- W2323500172 hasRelatedWork W2802267356 @default.
- W2323500172 hasRelatedWork W2953085761 @default.
- W2323500172 hasRelatedWork W2966967001 @default.
- W2323500172 hasRelatedWork W3099975487 @default.
- W2323500172 hasRelatedWork W3164087027 @default.
- W2323500172 hasRelatedWork W410898503 @default.
- W2323500172 isParatext "false" @default.
- W2323500172 isRetracted "false" @default.
- W2323500172 magId "2323500172" @default.
- W2323500172 workType "article" @default.