
feat-thompson pramey

ganitamadhye, feat-thompson pramey kinwa visham kram pramey asey sangato qee visham kramacha pratyek maryadit gut sodavata yenyajoga aahe. heey siddha jhaale.
itihas.
 assa andaj lavala qee pratyek nonbellion maryadit sadhya gatacha kram summ asato. maryadit sopya gatanchya vargikaranasathi aadhar mhanoon sadhya gatanchya antarbhavanchya kendrikaranacha vapar karanyachi soochana kelee gelee, kaaran braur-faller pramey darshavito qee antarvahachya dilelya kendrikaranashi maryadit sopya gatanchi keval maryadit sankhya aahe. visham kramachya gatamadhye konatehi antarvirodh nasatat, mhanoon brauercha karyakram paar padnyasathi pratham heey darshavine aavashyak aahe qee gair-chakriy maryadit sopya gatanna kadhihi visham kram nasato. heey visham kramanche gut sodavata yenyajoge aahet heey darshavinyaitakech aahe, jeey fitt aanee thompson yanni siddha kele.
bernsidechya andajavar hallah see. aii. gatancha abhyas karnanyanni suru keela hota; heey asey gut aahet qee pratyek kshullak nasalelya ghatakache kendrikaran abelian aahe. eka agraganya shodhanibandhat tyanni dakhavun dile qee visham kramache serve see. aii. gut sodavata yenyajoge aahet. (nantar tyanni serve sadhya see. aii. gatanche aanee adhik samanyatah serve sopya gatanche vargikaran kele, jase qee konatyahi hastakshepala kendrasthani thevana samanya 2-sayalo upasamuh asato, jyaa prakriyet khote bolananya sopya gatanche durlakshit kutumb shodhale jaate, jyanna aata suzuki gut mhanatat.)
 see. aine. gatanchya kutumbasathi suzukiche kaam vistarit kele; heey asey gut aahet qee pratyek kshullak nasalelya ghatakache kendrikaran nilpotent aahe. tyanni dakhavun dile qee visham kramacha pratyek see. aine. gut sodavata yenyajoga aahe. tyancha purava suzukichya puravyasarkhach aahe. hii sumare 17 prushthe lamb hotee, jee tyaa velee gut siddhantatil puravyasathi khoop lamb asalyache manale jaat hote.
yaa prakriyetil pudhil payari mhanoon feat-thompson pramey vicharat ghetala jaau shakatoh teey darshavtat qee visham kramacha konatahi gair-chakriy sadha gut nahee, jyamule pratyek yogya upasamuh sodavata yeil. heey siddha karate qee visham kramacha pratyek maryadit gut sodavata yenyajoga aahe, kaaran kiman prati-udaharan mhanoon eka sadha gut asane aavashyak aahe jenekarun pratyek yogya upasamuh sodavata yenyajoga asel. jaree purava see. aii. pramey aanee see. aine. pramey yasarkhyach samanya ruparesheche anusaran karat asala, taree tapasheel khoopach adhik klisht aahet. antim pepper 255 panancha aahe.
puravyache mahatva.
feat-thompson prameyane dakhavun dile qee, pratyek nonbellion sadhya gatache eka antarbhav asalyane, antarvirodhanche kendrikarak vaparoon maryadit sopya gatanche vargikaran shakya asoo shakate. tyanni tyanchya puravyamadhye sadar keleli anek tantre, visheshtah sthanik vishleshanachi kalpana, vargikaranat vaparlya jaanarya sadhananmadhye pudhe vikasit kelee gelee. puravacha kadachit sarvat krantikari pailu mhanje tyachi lambih fitt-thompson peparchya aadhi, gut siddhantatil kahee yuktivad kahee pananpeksha jaast lamb hote aanee bahutek eka divasat vachata yet hote. itakya dirgh yuktivadanmule kaam houu shakate heey ekada gut siddhantkaranna samajale qee, shekado pananchi kagadpatre eka malika disu lagali. yapaiki kahinni agadi fitt-thompson pepardekhil qamee keela; michael ashbacker aanee stephen dii. kwasithin gatanvaril smith 1,221 prushthe lamb hota.
puravyache punaravalokan.
anek ganitshastradnyanni mool feat-thompson puravyache kahee bhag sope kele aahet. tathapi, yaa serve sudharana kahee pramanat sthanik aahet; yuktivadachi jaagtik rachana ajunahi tashich aahe, parantu yuktivadanche kahee tapasheel sope kele gele aahet.
haah saralikrut purava done pustakanmadhye prakashit karnyat aala aaheh, jyamadhye varn siddhant vagalata serve kahee samavisht aahe aanee, jyamadhye varn siddhant samavisht aahe. haah sudharit purava ajunahi khoop katheen aahe aanee mool puravyapeksha lamb aahe, parantu adhik aaramat shailit lihila aahe.
september 2012 madhye georges gonthiyar aanee microsoft research aanee inariyatil sahkari sanshodhakanni see. oo. kyu. proof sahayyakane tapasalela eka purnapane aupcharik purava jaheer keela.
puravyachi ruparesha.
feat-thompson pramey thet varnan karnyaivaji, suzukichya see. aii. prameyache varnan karane aanee nantar see. aine.-pramey aanee visham kram prameyasathi aavashyak asalelya kahee vistaranvar bhashya karane sope aahe. purava teen payyanmadhye vibhagala jaau shakato. aapan 'jee' haah visham kramacha eka gair-abelian (kiman) sadha gut asoo deto joou see. aii. atinche samadhan karato. visham krampatrakachya adhik tapshilvar pradarshanasathi kinwa kinwa pahaa.
payari 1. 'jee' gatachya sanrachaneche sthanik vishleshan.
see. aii. chya babatit heey sope aahe kaaran 'aaa' haah 'buub' saha pravas karato haah sambandh olakh nasalelya ghatkanvar samatulya sambandh aahe. tyamule ghatak samatulya varganmadhye vibhagale jaatat, jenekarun pratyek samatulya varg haah kamal abelian upasamuhatil gair-olakh ghatakancha sanch asato. yaa kamal abelian upasamuhanche samanyikaran karnare nemke 'jee' chey kamal yogya upasamuh asalyache disun yete. heey samanyikaran karnare heey frobanius gut aahet jyancha varn siddhant vajavipane pardarshak aahe aanee varn preranasah hatalanisathi yogya aahe. tasech, mukhya vibhajkancha sanch ."jee". jyaa abhajyankannusar vibhagani kelee jaate, jeey kamal abelian upasamuhanchya vishisht sanyugma varganchya kramanna vibhajit karatat. ."jee".. mukhya vibhajkanche vibhajan karnyacha haah namuna ."jee". vishisht sabhagruh upasamuhanchya sanyugma vargannusar (sabhagruh upasamuh mhanje jyachi kramvari aanee nirdeshank tulanene avibhajya aahe) jeey 'jee' chya kamal upasamuhanshi (sanyugmateparyant) sambandhit aahe, teey feat-holl-thompson see. aine.-pramey aanee feat-thompson visham-kram pramey yaa donhi puravyanmadhye punaravrutti kele jaate. pratyek kamal upasamuh 'm' madhye eka vishisht nilpotant holl upasamuh 'm' σ asato jyamadhye 'm' madhye samanyikaran asate, jyachi kramvari σ ('m') sanch tayar karananya vishisht avibhajyanni vibhajya asate. jarr aanee keval jarr sanch σ ("m") samaan asateel aanee jarr teey sanyugmit nastil tarr sanch σ ("m") vegale asateel, tarr done kamal upasamuh sanyugmit hotat. g" chya kramane bhag denara pratyek avibhajya ghatak σ ("m") yaa eka sanchat yeto. mhanoon "g" chya kramane vibhagnanya avibhajyanchi samatulya varganmadhye vibhagani kelee jaate, jee kamal upasamuhanchya sanyugma varganshi sambandhit aahet. see. aine.-prakaranacha purava haah see. aii.-prakaranapeksha aadhich lakshaniyaritya adhik katheen aaheh done bhinn silau upasamuh olakhamadhye chhedatat heey siddha karane hii mukhya atirikt samasya aahe. visham-kram siddhantachya puravyacha haah bhag 100 hoon adhik niyatkalik prushthe gheto. eka mahattvachi payari mhanje thompson advitiyata siddhantacha purava, jyamadhye asey namood kele aahe qee kiman 3 samanya shreniche abelian upasamuh eka adviteey kamal upasamuhat asatat, jyacha arth assa aahe qee jyaa moolankansathi sayalo "pii"-upasamuhanna jastit jaast 2 samanya shreni asate, tyaa "pii" chaa swatantrapane vichar karane aavashyak aahe. benderne nantar benderchya paddhaticha vapar karoon advitiyatechya siddhantacha purava sulabh keela. tarr see. aine.-prakaranat, parinami yenare kamal upasamuh 'emm' ajunahi frobanius gut aahet, visham-kram siddhantachya puravyat aadhalanaya kamal upasamuhanna yapudhe hii rachana asanyachi aavashyakta nahee aanee tyanchya sanrachaneche aanee parasparsanvadache vishleshan 5 sambhavya prakarche kamal upasamuh tayar karate, jyanna prakar i, ii, iii, IV, v mhanatat. prakar I upasamuh heey "frobanius prakar" chey asatat, jeey frobanius gatache thodese samanyikaran aahe aanee kharey tarr nantar puravyanmadhye frobanius gut asalyache darshavile gele aahe. tyanchyakade "m" f "′u" hii rachana aahe jithe "m" f "haah sarvat motha samanya nilpotant holl upasamuh aahe aanee" u "chaa upasamuh" u "0 aahe jyacha samaan ghatank aahe, mhanje" m "f" ′u "0 haah curnell" m "f" asalela eka frobenius gut aahe. prakar II, III, IV, v heey serve 3-charananche gut aahet, jyanchi rachana "m" f "" u "" "w" "1 aahe, jethe" m "" f "" u "haah" m "chaa vyutpann upasamuh aahe". prakar II, III, IV aanee V madheel upavibhag khalilpramane upasamuh 'yuu' chya sanrachanevar aanee antarbhut karnyavar avalambun asatoh
maximal upasamuhanche done varg vagalata serve varg I prakarache aahet, parantu maximal upasamuhanche done atirikt varg dekhil asoo shakatat, eka prakar II aanee eka prakar II, III, IV kinwa V.
payari 2. 'jee' chaa varn siddhant.
jarr x heey see. aii. gatatil 'jee' chya kamal abelian upasamuh 'aii' chya samanyikaran 'etch' chey irreducible varn asel, tyachya karnalmadhye 'aii' nasel, tarr aapan x laa 'jee' chya y varnat prerit karoo shakato, jeey apariharyapane irreducible nahee. jee" chya dnyat sanrachanemule, "jee" chya olakh ghatakachya vyatirikt sarvanvar vayachi varn moolye shodhane sope aahe. yacha arth assa qee jarr x1 aanee x2 hii "h" aanee y1 aanee y2 hii done irreducible akshare asateel, tarr y1 − y2 heey sambandhit prerit akshare asateel, aanee tyachya normchi ganana kelyane asey disun yete qee haah farak aahe "g" chya done irreducible aksharancha (heey kadhikadhi "h" chya sandarbhat "g" chee apavadatmak akshare mhanoon olakhale jaatat). mojanicha yuktivad darshavito qee 'jee' chey pratyek kshullak-aparivartaniy varn 'jee' chya kahee kamal abelian upasamuhanchya samanyikaranashi sambandhit apavadatmak varn mhanoon agadi ekada udbhavate. asach yuktivad (parantu abelian holl upasamuhanchya jaagi nilpotent holl upasamuh) see. aine.-prameyachya puravyat karya karato. tathapi, visham-kram prameyachya puravyamadhye, upasamuhanchya varnanmadhun 'jee' chee varn tayar karnyasathiche yuktivad adhik najuk aahet aanee varn preranapeksha varn ringjamadhil deed isometrycha vapar karatat, kaaran kamal upasamuhanchi rachana adhik klisht asate aanee teey qamee pardarshak paddhatine antarbhut asatat. apavadatmak varnanchya siddhantachi jaaga deed isometrycha vistar karnyasathi varnanchya susangat sanchachya siddhantane ghetali jaate. sthoolpane sangayache tarr, haah siddhant mhanato qee joparyant samavisht gatanchi vishisht achook rachana nasate toparyant deed isometry vadhavali jaau shakate. deed, sibley aanee pieterfalvimule charitra siddhant yaa sopya aavruttiche varnan kele.
payari 3. antim virodhabhas.
payari 2 paryant, aamchyakade see. aii. gut "jee" chya varn saraniche sampoorn aanee achook varnan aahe. hyatoon, aanee 'jee' chee visham kramvari aahe yaa vastusthiticha vapar karoon, andaj prapt karnyasathi pureshi mahitee upalabdh aahe ."jee". aanee 'jee' sope aahe yaa gruhitakachya virodhabhasashi julavun ghya. yuktivadacha haah bhag see. aine.-gut prakaranat ashach prakare karya karato.
tathapi, feat-thompson prameyachya puravyanusar, hii payari (nehmipramane) khoopach adhik klisht aahe. varn siddhant keval payari 1 nantar uralelya kahee sambhavya sanrachananna door karato. pratham teey darshavtat qee prakar I chey kamal upasamuh heey serve frobanius gut aahet. jarr serve kamal upasamuh prakar I asateel tarr see. aine. prakaranasarkhach yuktivad darshavito qee gut "jee" haah visham-kramatil kiman sadha gut asoo shakat nahee, mhanoon prakar II, III, IV kinwa v chya kamal upasamuhanche nemke done varg aahet. urvarit bahutansh purave aata yaa done prakarchya kamal upasamuh 's' aanee 't' aanee tyanchyamadhil sambandhanvar laksh kendrit karatat. adhik varn-saiddhantik yuktivad darshavtat qee teey 4 kinwa 5 prakarche asoo shakat naheet. done upasamuhanchi eka achook rachana aaheh upasamuh 's' haah 'p' q '×' q '× (' p 'q'-1)/('p'-1) kramacha aahe aanee tyat 'x' → 'x' σ '+' b 'yaa swarupachya' p 'q' kramachya maryadit kshetrachya antarnihit sanchachya serve automorphismcha samavesh aahe, jethe 'a' chaa niyam 1 aahe aanee 'σ' haah maryadit kshetracha automorphism aahe, jithe 'p' aanee 'q' heey bhinn avibhajya aahet. tii' chya kamal upasamuhat 'pii' aanee 'kyu' ulatya swarupachi rachana aahe. s' aanee 't' heey upasamuh jawalun jodalele aahet. p"> "q" ghetalyas, ekhada asey darshavu shakato qee kramanusar ("p" q "-1)/(" p "-1) chaa" s "chaa chakriy upasamuh, kramanusar (" q "p"-1)/("q"-1) chya "t" chya chakriy upasamuhatil upasamuhasah sanyugmit aahe. (visheshtah, pahili sankhya dusyala vibhajit karate, mhanoon jarr feat-thompsoncha andaj kharaa asel tarr too asey mhanoo shakel qee heey houu shakat nahee aanee yacha vapar yaa tappyavar purava purn karnyasathi keela jaau shakato. matra, haah andaj adyap apramanit aahe.)
jee" yaa gatala varn siddhant lagoo karnyapasoon nishkarsh assa aahe qee "jee" chee khaleel rachana aaheh "pii"> "kyu" asha avibhajya aahet qee ("pii" kyu "-1)/(" pii "-1) heey" pii "-1 chey sahadhikaram aahe aanee" jee "chaa ardh-nirdeshit utpadan" puu "dware dilela upasamuh aahe jithe" pii "haah" pii "" kyu "aanee" yuu "yaa tyachya manak 1 chya ghatakanchya kramachya maryadit kshetracha yogatmak gut aahe. shivay" jee "madhye" pii "chya kramankacha abelian upasamuh" kyu "aahe jyamadhye" vaay "ghatak asato, mhanje" pii "0" heey "kyu" aanee ("pii" 0) vaay "samanya karate, jethe" pii "haah pii" chya maryadit shrenichya kshetracha samooh aahe. ("pii" = 2 sathee samaan sanrachana ess. ell. 2 (2 "kyu") gatamadhye udbhavate, jyamadhye "puu" haah varchya trikoni matrixcha borel upasamuh aanee sootra _ 1 dware tayar kelelya kram 3 chaa upasamuh "kyu" aahe) heey antim prakaran door karnyasathi, thompsonne generator aanee sambandhansah kahee bhitidayakpane klisht hatalanicha vapar keela, jeey nantar sopya karnyat aale, jyancha yuktivad punarutpadit keela gela. purava, "p" q "kramachya maryadit kshetratil" a "ghatakanchya sanchachi tapasani karato, mhanje" a "aanee 2-a yaa doghanmadhyehi niyam 1 aahe. pratham yaa sanchacha 1 vyatirikt kiman eka ghatak aahe heey tapasate. nantar" g "gatatil generator aanee sambandhancha vapar karoon katheen yuktivad darshavito qee sanch ulatya ghet asatana bund keela aahe. jarr "a" sanchamadhye asel aanee 1 chya barobaricha nasel tarr bahupadi n ((1-"a") "x" + 1)-1 chee degree "q" asel aanee f "p" madheel "x" ghatkandware kiman "p" bhinn mule dilee jaatil, yaa vastusthiticha vapar karoon qee "x" → 1/(2-"x") sanch swatach mapp karato, mhanoon "p" ≤ "q", "p"> "q" yaa gruhitkala virodh karato.
vichitratecha vapar.
jee' gatacha kram visham aahe hii vastusthiti puravyat anek thikani khalilpramane vaparali jaate.