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The Burnside Problem: Rips’ Method for Arbitrary Ranksдипломная работа (Магистр)
- Научный руководитель: Белов Алексей Яковлевич
- Автор: Белецкий Антон Андреевич
- Тип: Магистр
- Год защиты: 2025
- Аннотация: In 1902 W. Burnside posed a problem which has been motivating the developments in Group Theory for more than a century. Since 1969, when Novikov and Adyan announced their result on infiniteness of Burnside groups for large odd exponents, several alternative methods for the proof have been found. This paper presents a novel approach to this notorious problem. We develop a method first proposed by E. Rips, continuing our previous work. In this paper we demonstrate the power of the method by applying it to two problems in the Group Theory: the Burnside problem, and the Plotkin problem, concerning nilpotency of Engel groups. Our contributions: a complete treatment of Burnside problem via this new approach ($n > 2^{15}$ odd), and a novel application of the method to Engel groups. These results demonstrate that this framework is not merely an alternative to the classical Adyan–Novikov construction but a versatile tool unifying two historically separate lines of research.
- Добавил в систему: Белов Алексей Яковлевич
Прикрепленные файлы
| № | Имя | Описание | Имя файла | Размер | Добавлен |
|---|---|---|---|---|---|
| 1. | Полный текст | beleckiy_aa_problema-bernsayda-metod-ripsa-dlya-proizvolnog… | 520,3 КБ | 6 июля 2025 [AlexeiBelov] | |
| 2. | Внешний отзыв | отзыв_квал_работа_Антона_Белецкого.pdf | 36,6 КБ | 6 июля 2025 [AlexeiBelov] |