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0401U000349,
к.ф.-м.н.
01-02-2001
o
The minimal systems of generators of finite hyperoctahedral, monomial, metasymmetric groups and groups of automatic permutations.
Sikora Vira Stepanivna,
popup.head Сущанський Віталій Іванович
popup.opponent Лиман Федір Миколайович
popup.opponent Боднарчук Юрій Вікторович
У роботi побудовано мiнiмальнi (за кiлькiстю елементiв) системи твiрних гiпероктаедральних, мономiальних та метасиметричних груп. Встановлено, що гiпероктаедральнi, мономiальнi та метасиметричнi рангу 2 групи є 2-породженими. Отримано верхнi оцiнки для дiаметрiв графiв Келi цих груп вiдносно побудованих двохелементних систем твiрних. Доведено, що метасиметричнi групи довiльного скiнченного рангу r>2 , є r-породженими, причому r -- найменше можливе таке число. Одержанi результати застосовано до дослiдження систем твiрних груп автоматних пiдстановок, якi дiють на множинi слiв фiксованої довжини або на множинi всiх слiв над даним алфавiтом. Дано коректне доведення нескiнченної породжуваностi основних груп автоматних пiдстановок, якi дiють на множинi всiх слiв над даним алфавiтом, чим виправлено помилки в ранiше опублiкованих доведеннях iнших авторiв.
2001-02-01
2020-04-04
Updated: 2025-12-14
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