Тип публикации: статья из журнала
Год издания: 2020
Идентификатор DOI: 10.1007/s40590-020-00290-3
Ключевые слова: finite group, subgroup functor, formation of groups, satellite of formation, totally composition formation, algebraic lattice of formations, formal language, hypergroup
Аннотация: In each group G, we select a system of subgroups tau(G) and say that tau is a subgroup functor if G is an element of tau(G) for every group G, and for every epimorphism phi : A -> B and any H is an element of tau(A) and T is an element of tau(B), we have H-phi is an element of tau(B) and T(phi-)1 is an element of tau(A). We consideПоказать полностьюr only subgroup functors tau such that for any group G all subgroups of tau(G) are subnormal in G. For any set of groups X, the symbol s(tau)(X) denotes the set of groups H such that H is an element of tau(G) for some group G is an element of X. A formation F is tau-closed if s(tau)(F) = F. The Frattini subgroup Phi(G) of a group G is the intersection of all maximal subgroups of G. A formation F is said to be solvably saturated if it contains each group G with G/Phi(N) is an element of F for some solvable normal subgroup N of G. Composition formations are precisely solvably saturated formations. It is shown that the lattice of all tau-closed totally composition formations is algebraic.
Журнал: BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA
Выпуск журнала: Vol. 26, Is. 3
Номера страниц: 1003-1014
ISSN журнала: 1405213X
Место издания: CHAM
Издатель: SPRINGER INTERNATIONAL PUBLISHING AG