Osnovy teorii Galua.

148 148 ~~~~IV. IlpuAiwzcenuq meopuu raiya NAl'SN =S, o4eBHAHO o6pa.3yeT rpynrny, KOTOPY10 mbM 6yareM H~Munn. H 0 p m a A1 H 3 a T o p 0 M SanmeHTa S H o6o3Hatiam liepe3 91. Pa3Aro)KKM no 91: (3.4) 0 = VZ+91T2 +..+91Tk. Touia m~acc 9iiemeHra S coI~eP)KHT POBHok gne 31meHTOB (3.5) 8, T71ST2,.. TJ-1S.TleRCTBHTeJIbHO, C 0lAH0ft CT0POHb1 KcaaKJbfl 3emeHT rpynnu MOW{HO flpeACTaBHTb B c)opme NTj, rue N-BJaemeHT rpynnu 91 Ho B CHJ1 cBOlCTBaZ HopmaJIH3aTopa HmeeT meCTO N- SN=S, OTKyaa~ (NTij7'S(NTi)= T- T'ST,, oricyxa MU 3aKmIOaem, WIO BCHKHtt mJ1meHT i~auero Kmracca COBnajiaeT C OJIHHM 143 3J1emeHTOB (3.5). C Japyrfot CTOpOHblj Bce BJnemeHTbl (3.5) pa3JIt~HMIb. aLeflCTBHTembHo,, eCCJH 6Ml HmeJIo meCTO Hanp~mep T7 'ST. = T7- ST, TO OTCtoaa ceA~OB~an 6Mi TJT7- STjT 1,T~-l-STij1 = 'ITO 03-atiano 6w~, WIO 3JIemeHT Tj T.J2 BXOA1HT B rpynny T, a 5TO HIPOTHBope'IHT n~paBH4.7 pa3aT0o )KeHHH rpynrz no noarpynnam. TaKH~M o6pLI3oM 'IHCJO 9JIemeHTOB B Ka)KJLM Knacce paBH0 HHaleK(Cy HOpmaa3JI4TOpa O.IHoro H3 9.TemeHTOB aToro Kilacca, T. e. eCTb A.eJIHTeJ~b nopujLca rpynnbi ~, tl. H T. ja. 4. T e o pe m a 76. Bcswag rpynrina, HO~5UaOK KOTOpoft eCmb Crenew, npoc~oro Lmcna., pa3pewlHma. f Rt 0K a 3aTe JIb C TBo0. HyCmb 11OpALK rpyirinbi ~)paBeH pm, rj~e pnpoC~oe 'iMcJIo. Pa3o6beM Bce 9J1emeHTM 9Toh rpyrnbi no K~accam; flyCTb Kaw>KI1t 143 9THX KiuiaccOB 6yhleT coJLepK3T COOTBeTCTBeHHo h1, h2),.. hi SalemeHTOB. Torara o'IeBHJ4HO HmeeT meCTO: (3.6) h + h2 +... +h. =pm. Ho0 Teopeme 75 icawaoe 143 qIiceni h, paBHO HJIH eJLHHHLue, HaH CTeneHH P. BMeCTe C Tem eJAHHliH4lFl 3JCmeHT He meHfIeTCH HH npH KaKHx npeo6pa3OBaHH5IX, a nOo~omy ero KJ1acc COCTOHT TOJ3bKO 143 OaHoro gneeMeH., T. e. hi= 1. ECJIH 6bM BCe OCTaJIIbHbe t~c~jia h,~ 6bmHn CTenleHF1Ml 7P, TO JIeBa$i tiaCrb pa~eHCT~a (3.6) He uAe.Wuaa~ 6W Ha p, a npa~a~i iaentmaCb 6bM, 'ro HeBo3MOM0H. Ho9TOMy cpe~aH ti~ceAl h, JLOJDHbl 6hlTb H KOM ome 'h JIena paB3Hbie eJmHHlmie. COOTBeTCTBy101utHe 3T1M 'IHcj1am h, 3JIemmHT rpynnb (5 COBHnIIaIOT CO BcemH CBOI4M1 cofiHwKHHbmMH BJIemeHTaMHI, T. e. nepeCTaHo19O'4Hbl CO BcemH 3J1emmaTmH rpynbi7 (55 CoOBicyrnHoCm TaKHX 3JemeHTOR COCTmBJie1T rpyuiny, Ha3bIBaemy1o u~e H T p o rpyfnni (5. LUeHTP 51BJ151TC5I oq-eBHILHo a6eqeBoj3 rpynnfto H BmeCTe C TeM HOpmamJHHjmM IeJHTeJnem IpyflrIM (5. MMHaK rpynnrii (5 nopfluua Pm Bcerxaa Hmme1T OTJ1HqHbe 01T e1IHIHH4oR rpynnfbi a6eneBuI HopmaJnbHMCe uelHTemlH.Lnora.HHTeJnbHwe K 9TfhM Jae1HTflmm FpynnblMmT1 Hme1OT Hl~pgLLKH, paBHbMC CTefieH51M P, a rIOTOMY OInllTb JAOJI)Hbl HmeTb OTJIH4qHbie 01' eJllHHqHoH0 roynflibi a6eiieBbi H0PMa1JlbHb1e JaenlHTeJ1H, H T. A. TaKmm o6pa3oM KOMHO03HLLHOHHh~fl pHXL rpynnfbi(5 COCTOHT 143 a6eneBuK 9qBeHbeB, a noToMy rpynraa (5 pa3petuHima, 'I. H T-. 3.5. Teriepb MbM mo}KeM BMlBeCTH yCJ10BHe Toro, 'ITo6bi KOPHH ypa3BHfHHlI I6Mml~ HanlIeHbl f1OCTpoeHH59MH n1ocpeaCTBOM ULHPKyJ151 H JlHHefliKH

/ 232
Pages

Actions

file_download Download Options Download this page PDF - Pages 137-156 Image - Page 137 Plain Text - Page 137

About this Item

Title
Osnovy teorii Galua.
Author
Chebotarev, Nikolaĭ Grigorʹevich, 1894-1947.
Canvas
Page 137
Publication
Leningrad,: Gos. tekhniko-teoreticheskoe izd-vo,
1934-
Subject terms
Galois theory

Technical Details

Link to this Item
https://name.umdl.umich.edu/acr5415.0001.001
Link to this scan
https://quod.lib.umich.edu/u/umhistmath/acr5415.0001.001/152

Rights and Permissions

The University of Michigan Library provides access to these materials for educational and research purposes. These materials are in the public domain in the United States. If you have questions about the collection, please contact Historical Mathematics Digital Collection Help at [email protected]. If you have concerns about the inclusion of an item in this collection, please contact Library Information Technology at [email protected].

DPLA Rights Statement: No Copyright - United States

Manifest
https://quod.lib.umich.edu/cgi/t/text/api/manifest/umhistmath:acr5415.0001.001

Cite this Item

Full citation
"Osnovy teorii Galua." In the digital collection University of Michigan Historical Math Collection. https://name.umdl.umich.edu/acr5415.0001.001. University of Michigan Library Digital Collections. Accessed June 25, 2025.
Do you have questions about this content? Need to report a problem? Please contact us.