Приводимые τ-замкнутые σ-локальные формации конечных групп с заданной структурой подформаций

Скрундь В. В.; Сафонова И. Н.

Приводимые τ-замкнутые σ-локальные формации конечных групп с заданной структурой подформаций

Скрундь В. В., Сафонова И. Н.

2025

Пусть $\mathfrak{F}$ и $\mathfrak{H}$ – некоторые $\tau$-замкнутые $\sigma$-локальные формации конечных групп. Через $\mathfrak{F}/^\tau_\sigma\mathfrak{H}\cap\mathfrak{F}$ обозначают решетку всех $\tau$-замкнутых $\sigma$-локальных формаций $\mathfrak{X}$ таких, что $\mathfrak{H}\cap\mathfrak{F}\subseteq \mathfrak{X}\subseteq \mathfrak{F}.$ Длину решетки $\mathfrak{F}/^\tau_\sigma\mathfrak{H}\cap\mathfrak{F}$ называют {\it $\mathfrak H^\tau_\sigma$-дефектом}, а при $\mathfrak{H}=(1)$ – формация всех единичных групп, {\it $l^\tau_\sigma$-длиной} формации $\mathfrak{F}$. Изучены общие свойства $\mathfrak H^\tau_\sigma$-дефекта $\tau$-замкнутых $\sigma$-локальных формаций, получено описание структурного строения приводимых $\tau$-замкнутых $\sigma$-локальных формаций, имеющих $\mathfrak H^\tau_\sigma$-дефект $\leq 2$ и $l^\tau_\sigma$-длину $\leq 3$.

Скрундь В. В., Сафонова И. Н. Приводимые τ-замкнутые σ-локальные формации конечных групп с заданной структурой подформаций. Труды Института математики НАН Беларуси. 2025;33(2):36-53.

Цитирование

Список литературы

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Источник

Информация

Автор

Скрундь В. В. Белорусский государственный университет
Сафонова И. Н. Белорусский государственный университет

Страницы

36-53

Год издания

2025

Ключевые слова

Коллекции

Труды Института математики НАН Беларуси