Matches in SemOpenAlex for { <https://semopenalex.org/work/W176020141> ?p ?o ?g. }
Showing items 1 to 95 of
95
with 100 items per page.
- W176020141 endingPage "137" @default.
- W176020141 startingPage "123" @default.
- W176020141 abstract "A group is usually input into a computer by specifying the group either using a presentation or using a generating set of permutations or matrices. Here we will emphasize the latter approach, referring to [Si3, Si4, Ser1] for details of the other situations. Thus, the basic computational setting discussed here is as follows: a group is given, specified as G = 〈X〉 in terms of some generating set X of its elements, where X is an arbitrary subset of either Sn or GL(d, q) (a familiar example is the group of Rubik’s cube). The goal is then to find properties of G efficiently, such as |G|, the derived series, a composition series, Sylow subgroups, and so on. When G is a group of permutations there is a very well-developed body of literature and algorithms for studying its properties (see Section 2). The matrix group situation is much more difficult, and is the focus of the remaining sections of this brief survey. Sections 4 and 5 discuss the case of simple groups, and section 6 uses these to deal with general matrix groups. We will generally emphasize the group-theoretic aspects of the subject, rather than ones involving implementation in the computer systems GAP [GAP4] or Magma [BCP]. Thus, the word “efficiently” used above will usually mean for us “in time polynomial in the input length of the problem” rather than “works well in practice”. One can ask for the relevance of such questions to finite group theory. Certainly computers have been involved in the construction of sporadic simple groups, as well as in the study of these and other simple groups. We will make a few comments concerning the expected uses in GAP and Magma of the results presented here. However, our point of view includes a slightly different aspect: the purely mathematical questions raised by computational needs have led to new points of view and new questions concerning familiar groups." @default.
- W176020141 created "2016-06-24" @default.
- W176020141 creator A5008727965 @default.
- W176020141 date "2003-03-01" @default.
- W176020141 modified "2023-09-25" @default.
- W176020141 title "Computing with matrix groups" @default.
- W176020141 cites W11109725 @default.
- W176020141 cites W135053117 @default.
- W176020141 cites W1493654001 @default.
- W176020141 cites W1531837867 @default.
- W176020141 cites W1537195693 @default.
- W176020141 cites W1654307529 @default.
- W176020141 cites W171553832 @default.
- W176020141 cites W1854352062 @default.
- W176020141 cites W185811670 @default.
- W176020141 cites W189760519 @default.
- W176020141 cites W192805940 @default.
- W176020141 cites W1964155237 @default.
- W176020141 cites W1964582653 @default.
- W176020141 cites W1968357081 @default.
- W176020141 cites W1969754062 @default.
- W176020141 cites W1976677460 @default.
- W176020141 cites W1979045682 @default.
- W176020141 cites W1991451613 @default.
- W176020141 cites W1998864653 @default.
- W176020141 cites W2009068805 @default.
- W176020141 cites W2015416631 @default.
- W176020141 cites W2020524208 @default.
- W176020141 cites W2021337234 @default.
- W176020141 cites W2036318904 @default.
- W176020141 cites W2047131975 @default.
- W176020141 cites W2053954083 @default.
- W176020141 cites W2071421100 @default.
- W176020141 cites W2072053864 @default.
- W176020141 cites W2090822074 @default.
- W176020141 cites W2103998840 @default.
- W176020141 cites W2113555467 @default.
- W176020141 cites W2119687749 @default.
- W176020141 cites W2121041602 @default.
- W176020141 cites W2127481669 @default.
- W176020141 cites W2128861872 @default.
- W176020141 cites W2158651754 @default.
- W176020141 cites W2168018634 @default.
- W176020141 cites W2184608745 @default.
- W176020141 cites W2248523876 @default.
- W176020141 cites W2492220597 @default.
- W176020141 cites W2500409599 @default.
- W176020141 cites W2622084132 @default.
- W176020141 cites W319610176 @default.
- W176020141 cites W64604990 @default.
- W176020141 cites W840050675 @default.
- W176020141 cites W3140594797 @default.
- W176020141 doi "https://doi.org/10.1142/9789812564481_0007" @default.
- W176020141 hasPublicationYear "2003" @default.
- W176020141 type Work @default.
- W176020141 sameAs 176020141 @default.
- W176020141 citedByCount "6" @default.
- W176020141 countsByYear W1760201412016 @default.
- W176020141 crossrefType "book-chapter" @default.
- W176020141 hasAuthorship W176020141A5008727965 @default.
- W176020141 hasBestOaLocation W1760201412 @default.
- W176020141 hasConcept C106487976 @default.
- W176020141 hasConcept C136119220 @default.
- W176020141 hasConcept C159985019 @default.
- W176020141 hasConcept C192562407 @default.
- W176020141 hasConcept C202444582 @default.
- W176020141 hasConcept C33923547 @default.
- W176020141 hasConcept C41008148 @default.
- W176020141 hasConceptScore W176020141C106487976 @default.
- W176020141 hasConceptScore W176020141C136119220 @default.
- W176020141 hasConceptScore W176020141C159985019 @default.
- W176020141 hasConceptScore W176020141C192562407 @default.
- W176020141 hasConceptScore W176020141C202444582 @default.
- W176020141 hasConceptScore W176020141C33923547 @default.
- W176020141 hasConceptScore W176020141C41008148 @default.
- W176020141 hasLocation W1760201411 @default.
- W176020141 hasLocation W1760201412 @default.
- W176020141 hasOpenAccess W176020141 @default.
- W176020141 hasPrimaryLocation W1760201411 @default.
- W176020141 hasRelatedWork W1588620092 @default.
- W176020141 hasRelatedWork W2348302509 @default.
- W176020141 hasRelatedWork W2366479660 @default.
- W176020141 hasRelatedWork W2391242524 @default.
- W176020141 hasRelatedWork W2783489612 @default.
- W176020141 hasRelatedWork W2987709379 @default.
- W176020141 hasRelatedWork W4226115390 @default.
- W176020141 hasRelatedWork W4288278617 @default.
- W176020141 hasRelatedWork W4299933897 @default.
- W176020141 hasRelatedWork W4320926010 @default.
- W176020141 isParatext "false" @default.
- W176020141 isRetracted "false" @default.
- W176020141 magId "176020141" @default.
- W176020141 workType "book-chapter" @default.