swabhaava sidhaantham

ganithashaasthrathil, kooduthal vyakthamaayi group sidhaanthathil, oru group praathinidhyatthinte swabhaavam oro group gadakavumaayum anubandha maatriksinte adayaalavumaayi bandhappeduthunna groupile oru pravarthanamaanu. praathinidhyathekkurichu avashya vivarangal kooduthal ghaneebhavicha roopathil kathaapaathram vahikkunnu. poornnamaayum pratheekangale adisthaanamaakkiyullathum praathinidhyangalude vyakthamaaya matricks saakshaathkaaramillaathe parimitha grouppukalude praathinidhya sidhaantham jorg frobinius thudakkathil vikasippichu. oru parimitha grouppinte sankeernamaaya praathinidhyam (isomorphism vare) athinte swabhaavathaal nirnnayikkappedunnathil ithu saadhyamaan. modular praathinidyangal" ennu vilikkappedunna positteev swabhaavathinte oru mekhalayilulla praathinidyangalulla sahacharyam kooduthal sookshumamaanu, ennaal richard brower eee kesilum pratheekangalude sakthamaaya sidhaantham vikasippichu. parimithamaaya grouppukalude gadanayekkurichulla niravadhi aazhathilulla sidhaanthangal modular praathinidhyangalude pratheekangal upayogikkunnu.
aaplikkeshanukal.
irreducible praathinidhyangalude pratheekangal oru grouppinte niravadhi pradhana gunangale encode cheiyunnu, athinaal athinte ghadana padikkaan ithu upayogikkaam. parimithamaaya lalithamaaya grouppukalude vargeekaranathil prateeka sidhaantham oru pradhana upakaranamaan. pheett-thompson sidhaanthathinte thelivukalude pakuthiyolam prateeka moolyangalulla sankeernamaaya kanakkukoottalukal ulkkollunnu. akshara sidhaantham upayogikkunna eluppavum ennaal ippozhum anivaryavumaaya phalangalil bensaidinte sidhaantham (bensaidinte sidhaanthathinte poornnamaayum group-saidhaanthika thelivu pinneedu kandethiyittundu, ennaal aaa thelivu bensaidinte yadhaartha thelivu kazhinju aranoottaandilere kazhinju vannu), oru parimithamaaya lalithamaaya groupinu athinte sailo-subgroupaayi oru saamaanyavalkkaricha quaternian group undaayirikkaan kazhiyillennu prasthaavikkunna richard brouyarudeyum mishiyo suzukiyudeyum sidhaantham enniva ulppedunnu.
nirvachanangal.
oru feeldinu mukalilulla oru parimitha-dimensional vekttar space ayirikkatte, oru grouppinte praathinidyamaayirikkate. nalkia functionaanu swabhaavam
evideyaanu adayaalam.
oru pratheekatthe irreducible allengil lalithamaaya praathinidhyamaanenkil irreducible ennu vilikkunnu. aksharatthinte alavu; swabhaavasavisheshathakal poojyathil ithu moolyathinu thulyamaanu. digri 1 ulla oru pratheekatthe leanier ennu vilikkunnu. parimithavum swabhaavasavisheshathakal poojyavum ullappol, pratheekatthinte kernel saadhaarana upavibhagamaananu
ithu krithyamaayi praathinidhyatthinte kernalaanu. ennirunnaalum, eee kathaapaathram pothuve oru group homomorphisamaanu.
swathukkal.
ganithashaasthraparamaaya gunangal.
ρ, σ enniva prathinideekarikkatte. appol thaazhepparayunna identittikal nilanilkkunnu

