
bahupadi perugudala samuuhaalapai gromov siddhaantam

rekhaganita samuuha siddhaantamlo, bahupadi perugudala samuuhaalapai gromov siddhaantam, modata mikhail gromov dwara niroopinchabadindi, parimita suuchika yokka nilpotent upa samuuhaalanu kaligi unna samuhaluga, "bahupadi" perugudala yokka parimitamgaa utpatti cheyabadina samuuhaalanu vargeekaristundi.
prakatana.
oka samuuham yokka vruddhi raetu anedi lakshanarahita vislaeshanha nundi baga nirvachinchabadina bhavana. oka parimitamgaa utpatti cheyabadina samuuham bahupadi perugudalanu kaligi undani cheppalante, garishtamgaa "n" vadda podavaina muulakaala sankhya (samaroopa utpatti samitiki sambandhinchi) bahupadi function "p" ("n") dwara sarihaddulugaa untundi. perugudala kramam" anedi atuvanti bahupadi function "p" yokka athi takkuva sthaayi.
oka nilpotent samuuham "zii" anedi gurtimpu upa samuuhamloo mugise diguva kendra shrenitho kuudina samuuham.
parimita suuchika kaligina nilpotent upasamuuham unte matrame, parimitamgaa utpatti cheyabadina samuuham bahupadi vruddhini kaligi untundani gromov siddhaantam perkondi.
nilpotent samuuhaala vruddhi raetlu.
gromov siddhaantaaniki daariteese vruddhi retlapai vistaaramaina saahityam undhi. joseph eah yokka munupati phalitam. g" anedi oka parimitamgaa utpatti cheyabadina nilpotent samuuham ayithe, aaa samuuham bahupadi perugudalanu kaligi untundani thodelu choopinchindi. vives giwark 'hetch mariyu swatantramgaa haiman baas (vividha rujuvulatho) bahupadi perugudala yokka khachitamaina kramaanni lekkinchaaru. g" anedi takkuva madhya shrenitho kuudina parimitamgaa utpatti cheyabadina nilpotent samuuhamgaa undanivvandi.
mukhyamgaa, coashant group "g" "k"/"g" "k" + 1 anedi finally generate cheyabadina abelian group.
baas-giwark suutram "g" yokka bahupadi perugudala kramam anie perkondi
ekkadah
mukhyamgaa, gromov siddhaantam mariyu baas-giwark suutram, oka parimitamgaa utpatti cheyabadina samuuham yokka bahupadi perugudala kramam ellappuduu oka puurnaamkam ledhaa anantam (udaaharanaku, binna saktulu minahayinchi) anie suuchistumdi.
gromov siddhaantam mariyu baas-guiwarch suutram yokka maroka manchi anuvartanam, finalityga utpatti cheyabadina abelian samuuhaala yokka pakshika-isometric drudatvamha finalityga utpatti cheyabadina abelian samuuhaaniki pakshika-isometric ayina edainaa samuuham parimita suuchika yokka uchita abelian samuuhaanni kaligi untundi.
gromov siddhaantam yokka rujuvulu.
eee siddhaantaanni niroopinchadaaniki gromov metrik spacela kosam convergensenu pravesapettaadu. ippudu gromov-housedorff convergence anie piluvabade eee convergence prastutam jyaamitiloo vistrutamgaa upayoginchabadutondi.
eee siddhaantaaniki saapekshamgaa saralamaina rujuvu brus cliner dwara kanugonabadindi. taruvaata, terrens tavo mariyu yehuda shalom cliner yokka rujuvunu tappanisarigaa praathamika rujuvutho paatu spashtamaina sarihaddulato siddhaantam yokka samskarananu roopondinchadaaniki savarinchaaru. brovillard, green mariyu tavo dwara pondina sumaru samuuhaala vargeekarana nundi kooda gromov siddhaantam anusaristundi. kriyaatmaka vislaeshanhaatmaka paddhatula aadhaaramgaa oka saralamaina mariyu sankshipta rujuvunu ojava istundi.
gyap ooha.
gromov siddhaantaaniki minchi, bahupadi perugudalaku paina, vaastavamgaa nilpotent samuuhaalanu itarula nundi vaeru chestu, parimitamgaa utpatti cheyabadina samuuhaaniki vruddhi varnapatamlo antaram undaa anie adagavacchu. adhikarikamga, dheeni ardham emitante, oka function formula _ 3 untundi, antey daani vruddhi function formula _ 4 ayithe matrame, oka finally generate group vaastavamgaa nilpotent avutundi. atuvanti siddhaantam shalom mariyu tavo dwara pondabadindi, konni formula _ 6 kosam spashtamaina function formula _ 5 thoo. intermediate groth (i.ii. superpolynomial mariyu subxponential rendoo) tappanisarigaa grigorchuk samuuham yokka saadhaaraneekaranalu, mariyu vegavantamaina vruddhi vidhulanu kaligi untaayi; kabatti telisina samuuhaalannii formula _ 8 thoo formula _ 7 kante vaegamgaa vruddhini kaligi untaayi, ikkada formula _ 9 anedi bahupadi suutram _ 10 yokka nijamaina muulam.
madhyantara vruddhi kaligina samuuhaala vruddhi retlapai nijamaina diguva parimiti suutram _ 11 anie oohinchabadindi. dheenini "gyap consector" anie pilustaaru.