Matches in SemOpenAlex for { <https://semopenalex.org/work/W2964332984> ?p ?o ?g. }
Showing items 1 to 90 of
90
with 100 items per page.
- W2964332984 abstract "It was shown by van Rees [Subsquares and transversals in latin squares, Ars Combin. 29B (1990) 193–204] that a latin square of order [Formula: see text] has at most [Formula: see text] latin subsquares of order [Formula: see text]. He conjectured that this bound is only achieved if [Formula: see text] is a power of [Formula: see text]. We show that it can only be achieved if [Formula: see text]. We also state several conditions that are equivalent to achieving the van Rees bound. One of these is that the Cayley table of a loop achieves the van Rees bound if and only if every loop isotope has exponent [Formula: see text]. We call such loops van Rees loops and show that they form an equationally defined variety. We also show that: (1) In a van Rees loop, any subloop of index 3 is normal. (2) There are exactly six nonassociative van Rees loops of order [Formula: see text] with a nontrivial nucleus and at least 1 with all nuclei trivial. (3) Every commutative van Rees loop has the weak inverse property. (4) For each van Rees loop there is an associated family of Steiner quasigroups." @default.
- W2964332984 created "2019-07-30" @default.
- W2964332984 creator A5019627457 @default.
- W2964332984 creator A5059332408 @default.
- W2964332984 date "2015-11-01" @default.
- W2964332984 modified "2023-09-26" @default.
- W2964332984 title "Loops with exponent three in all isotopes" @default.
- W2964332984 cites W131257252 @default.
- W2964332984 cites W1482309519 @default.
- W2964332984 cites W1603036561 @default.
- W2964332984 cites W1969156863 @default.
- W2964332984 cites W1979980641 @default.
- W2964332984 cites W1982319230 @default.
- W2964332984 cites W2020002518 @default.
- W2964332984 cites W2089456700 @default.
- W2964332984 cites W2105475350 @default.
- W2964332984 cites W2334904592 @default.
- W2964332984 cites W2603486134 @default.
- W2964332984 cites W2963385025 @default.
- W2964332984 cites W2965457536 @default.
- W2964332984 cites W4244733665 @default.
- W2964332984 cites W4249735382 @default.
- W2964332984 cites W812043222 @default.
- W2964332984 doi "https://doi.org/10.1142/s0218196715500356" @default.
- W2964332984 hasPublicationYear "2015" @default.
- W2964332984 type Work @default.
- W2964332984 sameAs 2964332984 @default.
- W2964332984 citedByCount "1" @default.
- W2964332984 countsByYear W29643329842019 @default.
- W2964332984 crossrefType "journal-article" @default.
- W2964332984 hasAuthorship W2964332984A5019627457 @default.
- W2964332984 hasAuthorship W2964332984A5059332408 @default.
- W2964332984 hasBestOaLocation W29643329842 @default.
- W2964332984 hasConcept C10138342 @default.
- W2964332984 hasConcept C114614502 @default.
- W2964332984 hasConcept C134306372 @default.
- W2964332984 hasConcept C138885662 @default.
- W2964332984 hasConcept C162324750 @default.
- W2964332984 hasConcept C175695255 @default.
- W2964332984 hasConcept C182306322 @default.
- W2964332984 hasConcept C184670325 @default.
- W2964332984 hasConcept C207467116 @default.
- W2964332984 hasConcept C2524010 @default.
- W2964332984 hasConcept C2780388253 @default.
- W2964332984 hasConcept C33923547 @default.
- W2964332984 hasConcept C41895202 @default.
- W2964332984 hasConcept C77553402 @default.
- W2964332984 hasConceptScore W2964332984C10138342 @default.
- W2964332984 hasConceptScore W2964332984C114614502 @default.
- W2964332984 hasConceptScore W2964332984C134306372 @default.
- W2964332984 hasConceptScore W2964332984C138885662 @default.
- W2964332984 hasConceptScore W2964332984C162324750 @default.
- W2964332984 hasConceptScore W2964332984C175695255 @default.
- W2964332984 hasConceptScore W2964332984C182306322 @default.
- W2964332984 hasConceptScore W2964332984C184670325 @default.
- W2964332984 hasConceptScore W2964332984C207467116 @default.
- W2964332984 hasConceptScore W2964332984C2524010 @default.
- W2964332984 hasConceptScore W2964332984C2780388253 @default.
- W2964332984 hasConceptScore W2964332984C33923547 @default.
- W2964332984 hasConceptScore W2964332984C41895202 @default.
- W2964332984 hasConceptScore W2964332984C77553402 @default.
- W2964332984 hasLocation W29643329841 @default.
- W2964332984 hasLocation W29643329842 @default.
- W2964332984 hasLocation W29643329843 @default.
- W2964332984 hasOpenAccess W2964332984 @default.
- W2964332984 hasPrimaryLocation W29643329841 @default.
- W2964332984 hasRelatedWork W1482547169 @default.
- W2964332984 hasRelatedWork W1811517255 @default.
- W2964332984 hasRelatedWork W1988036966 @default.
- W2964332984 hasRelatedWork W2008014193 @default.
- W2964332984 hasRelatedWork W2056137755 @default.
- W2964332984 hasRelatedWork W2101325629 @default.
- W2964332984 hasRelatedWork W2249760657 @default.
- W2964332984 hasRelatedWork W2272337235 @default.
- W2964332984 hasRelatedWork W2325821856 @default.
- W2964332984 hasRelatedWork W2483594352 @default.
- W2964332984 hasRelatedWork W2559811601 @default.
- W2964332984 hasRelatedWork W2564370940 @default.
- W2964332984 hasRelatedWork W2592377922 @default.
- W2964332984 hasRelatedWork W2754436575 @default.
- W2964332984 hasRelatedWork W2788395808 @default.
- W2964332984 hasRelatedWork W2962839324 @default.
- W2964332984 hasRelatedWork W2963519231 @default.
- W2964332984 hasRelatedWork W2964031089 @default.
- W2964332984 hasRelatedWork W3128764743 @default.
- W2964332984 hasRelatedWork W3160248697 @default.
- W2964332984 isParatext "false" @default.
- W2964332984 isRetracted "false" @default.
- W2964332984 magId "2964332984" @default.
- W2964332984 workType "article" @default.