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Walter theorem

Matematikada Valter teoremasitomonidan isbotlangan John H. Walter (1967, 1969), tasvirlaydi cheklangan guruhlar kimning Sylow 2-kichik guruh bu abeliya. Bender (1970) ishlatilgan Bender usuli oddiyroq dalil berish.

Bayonot

Valter teoremasida, agar shunday bo'lsa, deyilgan G cheklangan guruh bo'lib, uning 2-sylow kichik guruhlari abeliya, keyin G/O(G) bor oddiy kichik guruh toq indeks, bu har biri 2-guruh yoki ulardan bittasi bo'lgan guruhlarning hosilasi oddiy guruhlar PSL2(q) uchun q = 2n yoki q = 3 yoki 5 mod 8 yoki Janko guruhi J1, yoki Ree guruhlari 2G2(32n+1).

Valter teoremasining dastlabki bayoni Rei guruhlarini to'liq aniqlamagan, ammo faqatgina tegishli guruhlarning Ree guruhlari singari kichik guruh tuzilishiga ega ekanligini ta'kidlagan. Tompson (1967, 1972, 1977) va Bombieri, Odlyzko va Hunt (1980) keyinchalik ularning barchasi Ree guruhlari ekanligini ko'rsatdi va Enguehard (1986) ushbu natijaning yagona ekspozitsiyasini taqdim etdi.

Adabiyotlar

  • Bender, Helmut (1970), "Abelyan Sylow 2-kichik guruhlari bo'lgan guruhlar to'g'risida", Mathematische Zeitschrift, 117: 164–176, doi:10.1007 / BF01109839, ISSN 0025-5874, JANOB 0288180
  • Bombieri, Enriko; Odlyzko, Endryu; Hunt, D. (1980), "Tompson muammosi (σ.)2=3)", Mathematicae ixtirolari, 58 (1): 77–100, doi:10.1007 / BF01402275, ISSN 0020-9910, JANOB 0570875
  • Enguehard, Mishel (1986), "Caractérisation des groupes de Ree", Asterisk (142): 49–139, ISSN 0303-1179, JANOB 0873958
  • Tompson, Jon G. (1967), "E ning tavsifiga qarab2*(q) ", Algebra jurnali, 7: 406–414, doi:10.1016/0021-8693(67)90080-4, ISSN 0021-8693, JANOB 0223448
  • Tompson, Jon G. (1972), "E ning tavsifiga qarab2*(q). II ", Algebra jurnali, 20: 610–621, doi:10.1016/0021-8693(72)90074-9, ISSN 0021-8693, JANOB 0313377
  • Tompson, Jon G. (1977), "E ning tavsifiga qarab2*(q). III ", Algebra jurnali, 49 (1): 162–166, doi:10.1016/0021-8693(77)90276-9, ISSN 0021-8693, JANOB 0453858
  • Uolter, Jon H. (1967), "Abelian Sylow 2-kichik guruhli 8-sonli guruhlar", Mathematicae ixtirolari, 2: 332–376, doi:10.1007 / BF01428899, ISSN 0020-9910, JANOB 0218445
  • Uolter, Jon H. (1969), "Abelian Sylow 2-kichik guruhlari bilan cheklangan guruhlarning tavsifi.", Matematika yilnomalari, Ikkinchi seriya, 89: 405–514, doi:10.2307/1970648, ISSN 0003-486X, JSTOR 1970648, JANOB 0249504