Osnovy teorii Galua.

~ 7' Pa3pewumbie 2pynlfbl 5 53 HopmaJnbHIM JaeJHTehnem Fpynnfbi 0. HO TaK KaK rpyrn-a.21 HHTpaH3HTHBHa, TO rpynria (0 He moKeT 6bITb B STOM caiyqae npHMIHTHBHOft. 14. TaKH-M o6pa3oM xaeiio npHBO.~tHTCfI K 113y4CHHIO paapelHHmhx 'pyinn?cflenHH Pk, raie, p-HpoCToe 'iircio. EcnH fpi4 3TOM rpyrnna 2 LUHKlnqeCKa5I, TO rpynria 03 onHTb HiMnpHMHT4TBHa. B camom jiejne, ID 9TOM cniyqae Torira rpyrina flBARfHCb eAIHHCTBeHHUM azeJIHTe.~em rpynni~f ~e Hop5LTiJ( /, JLOJDKBa 6bITb HOPmaJlbHbIM awJIeneIm rpynribI (, 6yayiRT1 B TO )Ke Bpemq HHTpaH3H4THBH~fl rpynnrtol. Paupemmmw1e rpynnbi CreneHH Pk 6bIJni HnpeameTOM HccjieAJLBaHHl MHworMX maTemaTIKOB, KaK Hanptimep ranrya, )Kopmaa (C. Jordan), I3eTTH (Betti), 0. 10. LIMHJLTa i4 JUp. H3 9THX 11ccAeJLBaffili BbITeKaeT, '4T0 3.ReCb Mbl He mo)KeM HaaeS5Tb~g$ Ha TaICoA npOCTOR~ pe3y~lbTaT, KaKoh mbi HmeeM B Ciiy ae pa3peIIHMbix rpyriri rHpoCTbIX cUeneHefl. H4meHHO, Mbl He noniy'aeM 3JaeCb aJ~jn Ka}K)aoft C~eneiiu oaiiofl rpynnbl TaKOrO, no09, xITo Kawaaq pa3pCLBHmaf rpynn~a 51BA15eTC% ee. )1eJ1TeJem. 15. Pa3pemu~mble FPYI1I~bl C~eneffm p2. PacCMOTpHM uiiis npumepa cjiy-,qaif n p2, ri-ie p HeqeT~oe npoC~oe 'iiicino. Fpynna ~, eCTI, He-IujIKQjjwecKaI a6en~eBa rpynna nop51JKa p2 H110H3TOMY A1OJI)KHa pair~~ B np~imoe npoH3BCJCHHe JLBYX ILHKIH14eclCI( pynrl nopmuua p: rue ~1j== J+ C,+ C12 +..+CP- ~ = + +C2+.+ Cp'. rlepenymepyem nepemeuiiaembie rpyninotI fCLMTAceyoaio6pa3om. 3yuaem o603Haqam Kma~IcJajA1 npeumeT 2SBYMq 3Ha'IumH neCpBb1f 3HaqOK Aojj )1CeH yKa3bIBaTb, B KaKwtI CH4CTeme HHTpaH3HTHBHOCTf4 Fpyrinbl ~2 HaxoJLHTCRI )iaaHHbflg HpeameT; BTOpofl We 3Ha4OIC yKa3bIBaeT CHCTemy HIHTpaH3H4THBHOCTI4 rpynubix ~i. HeTpyaHO flOHIM, 'ITO Kaw)KJaia 113 CHiCTem HHTpaH3I4THBHOCTH o6euix rpyrin ~1, ~2 COCTOI4T 113 p InpeulmeTOB, B cHJ1y tiero o6a 3Ha4Ka Z1OJIYKHbl npo6eraTm p 3Ha'eHfi4Il, CKa)Kem 0, 1, 2,..., p - 1. 3auaalmem o6oHx 3H&HKOB npejimeT BR7OJIHe onpeI~eaJUeTC5, TaK KaK 11 'IHCJO rIpe~meTOB 11 4FIcjio i(om6HHaruHfl 3Ha1INOB p3aRHbl 03HOMY H TOMT )Ke qH4CJIy p2, H ecCJH 6b1 cyILueCTBOBaJIH uAM pa3.TIH'IHbIX npeaLmeTa c o6ujiUM 3H Fa'I1<amF, TO AOJDKHa 6biua 6bi cyu4eCTBOBaTb KOm~Mawniaug 3Ha1IKOB, He 11meioma%~ COOTBeTCTBYIOUI~rO npeameTa, T. e. B KawaolO r-pynhie mo)KHo 6b1.no 6b1 BbU[CJHTb no CH1CTeme HHTpaH3HTHIBHOCTH., KOTopbie BC coaepwiaT oftmw npearmeToB. Ho BTO iieBO3MO2IHO, TaK KmK eCCHI rIOCTaHOBma C== C,1C2~ n~peBOaHJT nepBblfi 3HaqOK i B nepBb1l1 3HatlOK j, TO nORCTaHOBKa C,' atejaeT TO weC Camoe, 1 npHi 3TOM OCTaBJIReT BTOpOII 3Haq'OK Ha meCTe; HO Tax Kai< rpyrina TpaH3HITHBHa, TO BbIXOaJHT, 'ITO mbI HmeeM BO3MO)KHOCTb IIepeXOJII1Tb BO BCe neCpBh1e 3HaqIKI, B TO We Bpemq OCTaBJIgq BTOPOAI 3H~aqO1( HeH43meHHbIM; TO We~ HmeeT meCTO H JUAR BTOpbIX 3Ha'IK03.

/ 232
Pages

Actions

file_download Download Options Download this page PDF - Pages 37-56 Image - Page 53 Plain Text - Page 53

About this Item

Title
Osnovy teorii Galua.
Author
Chebotarev, Nikolaĭ Grigorʹevich, 1894-1947.
Canvas
Page 53
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/acr5415.0001.001/57

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 17, 2025.
Do you have questions about this content? Need to report a problem? Please contact us.