Matches in SemOpenAlex for { <https://semopenalex.org/work/W2979403500> ?p ?o ?g. }
Showing items 1 to 100 of
100
with 100 items per page.
- W2979403500 abstract "A subset of a group invariably generates the group if it generates even when we replace the elements by any of their conjugates. In a 2016 paper, Pemantle, Peres and Rivin show that the probability that four randomly selected elements invariably generate $S_n$ is bounded away from zero by an absolute constant for all $n$. Subsequently, Eberhard, Ford and Green have shown that the probability that three randomly selected elements invariably generate $S_n$ tends to zero as $n rightarrow infty$. In this paper, we prove an analogous result for the finite classical groups. More precisely, let $G_r(q)$ be a finite classical group of rank $r$ over $mathbb{F}_q$. We show that for $q$ large enough, the probability that four randomly selected elements invariably generate $G_r(q)$ is bounded away from zero by an absolute constant for all $r$, and for three elements the probability tends to zero as $q rightarrow infty$ and $r rightarrow infty$. We use the fact that most elements in $G_r(q)$ are separable and the well-known correspondence between classes of maximal tori containing separable elements in classical groups and conjugacy classes in their Weyl groups." @default.
- W2979403500 created "2019-10-18" @default.
- W2979403500 creator A5084001366 @default.
- W2979403500 date "2019-10-08" @default.
- W2979403500 modified "2023-09-25" @default.
- W2979403500 title "Invariable generation of finite classical groups" @default.
- W2979403500 cites W11109725 @default.
- W2979403500 cites W1736900933 @default.
- W2979403500 cites W1972196995 @default.
- W2979403500 cites W1995703230 @default.
- W2979403500 cites W1998261334 @default.
- W2979403500 cites W2046433533 @default.
- W2979403500 cites W2064858845 @default.
- W2979403500 cites W2076973717 @default.
- W2979403500 cites W2078590838 @default.
- W2979403500 cites W2088381458 @default.
- W2979403500 cites W2113856480 @default.
- W2979403500 cites W2151340275 @default.
- W2979403500 cites W2324705588 @default.
- W2979403500 cites W2427028772 @default.
- W2979403500 cites W2963252403 @default.
- W2979403500 cites W2963607991 @default.
- W2979403500 cites W3106463960 @default.
- W2979403500 hasPublicationYear "2019" @default.
- W2979403500 type Work @default.
- W2979403500 sameAs 2979403500 @default.
- W2979403500 citedByCount "2" @default.
- W2979403500 countsByYear W29794035002021 @default.
- W2979403500 countsByYear W29794035002022 @default.
- W2979403500 crossrefType "posted-content" @default.
- W2979403500 hasAuthorship W2979403500A5084001366 @default.
- W2979403500 hasConcept C114614502 @default.
- W2979403500 hasConcept C118615104 @default.
- W2979403500 hasConcept C121332964 @default.
- W2979403500 hasConcept C134306372 @default.
- W2979403500 hasConcept C138885662 @default.
- W2979403500 hasConcept C164226766 @default.
- W2979403500 hasConcept C187915474 @default.
- W2979403500 hasConcept C199360897 @default.
- W2979403500 hasConcept C202444582 @default.
- W2979403500 hasConcept C2777027219 @default.
- W2979403500 hasConcept C2777404646 @default.
- W2979403500 hasConcept C2780813799 @default.
- W2979403500 hasConcept C2781311116 @default.
- W2979403500 hasConcept C33923547 @default.
- W2979403500 hasConcept C34388435 @default.
- W2979403500 hasConcept C35661339 @default.
- W2979403500 hasConcept C41008148 @default.
- W2979403500 hasConcept C41895202 @default.
- W2979403500 hasConcept C62520636 @default.
- W2979403500 hasConcept C70710897 @default.
- W2979403500 hasConcept C87945829 @default.
- W2979403500 hasConceptScore W2979403500C114614502 @default.
- W2979403500 hasConceptScore W2979403500C118615104 @default.
- W2979403500 hasConceptScore W2979403500C121332964 @default.
- W2979403500 hasConceptScore W2979403500C134306372 @default.
- W2979403500 hasConceptScore W2979403500C138885662 @default.
- W2979403500 hasConceptScore W2979403500C164226766 @default.
- W2979403500 hasConceptScore W2979403500C187915474 @default.
- W2979403500 hasConceptScore W2979403500C199360897 @default.
- W2979403500 hasConceptScore W2979403500C202444582 @default.
- W2979403500 hasConceptScore W2979403500C2777027219 @default.
- W2979403500 hasConceptScore W2979403500C2777404646 @default.
- W2979403500 hasConceptScore W2979403500C2780813799 @default.
- W2979403500 hasConceptScore W2979403500C2781311116 @default.
- W2979403500 hasConceptScore W2979403500C33923547 @default.
- W2979403500 hasConceptScore W2979403500C34388435 @default.
- W2979403500 hasConceptScore W2979403500C35661339 @default.
- W2979403500 hasConceptScore W2979403500C41008148 @default.
- W2979403500 hasConceptScore W2979403500C41895202 @default.
- W2979403500 hasConceptScore W2979403500C62520636 @default.
- W2979403500 hasConceptScore W2979403500C70710897 @default.
- W2979403500 hasConceptScore W2979403500C87945829 @default.
- W2979403500 hasLocation W29794035001 @default.
- W2979403500 hasOpenAccess W2979403500 @default.
- W2979403500 hasPrimaryLocation W29794035001 @default.
- W2979403500 hasRelatedWork W1975976439 @default.
- W2979403500 hasRelatedWork W2016341899 @default.
- W2979403500 hasRelatedWork W2054165505 @default.
- W2979403500 hasRelatedWork W2103812807 @default.
- W2979403500 hasRelatedWork W2113138744 @default.
- W2979403500 hasRelatedWork W2146783382 @default.
- W2979403500 hasRelatedWork W2241896673 @default.
- W2979403500 hasRelatedWork W2345533269 @default.
- W2979403500 hasRelatedWork W2397173681 @default.
- W2979403500 hasRelatedWork W2739516390 @default.
- W2979403500 hasRelatedWork W2756596059 @default.
- W2979403500 hasRelatedWork W2774559945 @default.
- W2979403500 hasRelatedWork W2898286603 @default.
- W2979403500 hasRelatedWork W2963713484 @default.
- W2979403500 hasRelatedWork W2963715885 @default.
- W2979403500 hasRelatedWork W2976462379 @default.
- W2979403500 hasRelatedWork W3047676064 @default.
- W2979403500 hasRelatedWork W3209059903 @default.
- W2979403500 hasRelatedWork W68102810 @default.
- W2979403500 hasRelatedWork W1941768332 @default.
- W2979403500 isParatext "false" @default.
- W2979403500 isRetracted "false" @default.
- W2979403500 magId "2979403500" @default.
- W2979403500 workType "article" @default.