Поліциклічна група

Поліциклічна група — група, що має поліциклічний ряд, тобто субнормальний ряд з циклічними факторами.

Властивості

  • Клас поліциклічних груп тотожний класу розв'язних груп з умовою максимальності для підгруп;
    • він замкнутий щодо переходу до підгруп, факторгруп і розширень.
  • Число нескінченних факторів у будь-якому поліциклічному ряді — інваріант поліциклічної групи (поліциклічний ранг).
  • Будь-яка поліциклічна група ізоморфно вкладається в групу матриць над кільцем цілих чисел; це дозволяє застосовувати в теорії поліциклічних груп методи алгебраїчної геометрії.
  • У всякій групі добуток двох локально поліциклічних нормальних підгруп — локально поліциклічна підгрупа.

Див. також

Джерела

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