ON A FINITE GROUP FACTORIZED BY CONDITIONALLY SEMINORMAL SUBGROUPS
##plugins.themes.bootstrap3.article.sidebar##
##plugins.themes.bootstrap3.article.main##
Анатацыя
The subgroups \(A\) and \(B\) are said to be \({\mathrm c}{\mathrm c}\)-permutable, if \(A\) permutes with \(B^x\) for some \(x \in \langle A, B \rangle \). A subgroup \(A\) of a finite group \(G\) is called conditionally seminormal in \(G\), if there exists a subgroup \(T\) of \(G\) such that \(G = AT\) and \(A\) is \({\mathrm c}{\mathrm c}\)-permutable with all subgroups of \(T\). The groups \(G = G_1 G_2 ... G_n\) with pairwise permutable subgroups \(G_1, ... , G_n\) such that \(G_i\) and \(G_j\) are conditionally seminormal in \(G_i G_j\) for any \(i, j \in \{ 1, ... , n \}, i \neq j \), are studied.
##plugins.themes.bootstrap3.article.details##
Бібліяграфічныя спасылкі
1. Ballester-Bolinches, A. Products finite groups / A. Ballester-Bolinches, R. Estaban-Romero, M. Asaad. – Berlin ; New York : Walter de Gruyter, 2010. – 334 p.
2. Huppert, B. Endliche Gruppen / B. Huppert. – Berlin : Springer-Verlag, 1967.
3. Asaad, M. On the supersolubility of finite groups / M. Asaad, A. Shaalan // Arch. Math. – 1989. – Vol. 53. – P. 318–326.
4. Guo, W. Conditionally Permutable Subgroups and Supersolubility of Finite Groups / W. Guo, K.P. Shum, A.N. Skiba // Southeast Asian Bull. Math. – 2005. – Vol. 29. – P. 493–510.
5. Trofimuk, A. A. Finite Groups with Given Systems of Conditionally Seminormal Subgroups~ / A. A. Trofimuk // Lobachevskii Journal of Mathematics. – 2024. – Vol. 45. – P. 6624–6632.
6. Huppert, B. Monomialle darstellung endlicher gruppen / B. Huppert // Nagoya Mathematical Journal. – 1953. – Vol. 3. – P. 93–94.
7. Doerk, K. Finite soluble groups / K. Doerk, T. Hawkes. – Berlin ; New York : Walter de Gruyter, 1992. – 899 p.
8. Монахов, В. С. О сверхразрешимом корадикале произведения субнормальных сверхразрешимых подгрупп / В. С. Монахов, И. К. Чирик // Сибирский математический журнал. – 2017. – Т. 58, № 2. – C. 353–364.
9. Kazarin, L. S. Factorizations of finite groups by solvable subgroups / L. S. Kazarin // Ukrainian Mathematical Journal. – 1991. – Vol. 43, nr 7–8. – P. 883–886.
10. Wielandt, H. Subnormalität in faktorisierten endlichen Gruppen / H. Wielandt // J. Algebra. – 1981. – Vol. 69. – P. 305–311.
11. Casolo, C. Acriterion for subnormality andWielandt complexes in finite groups / C. Casolo // J. Algebra. –1994. – Vol. 169. – P. 605–624.
12. Княгина, В. Н. Конечные группы с полунормальными подгруппами Шмидта / В. Н. Княгина, В. С. Монахов // Алгебра и логика. – 2007. – Т. 46, № 4. – C. 448–458.
13. Monakhov, V.S. On finite factorized groups with permutable subgroups of factors / V. S. Monakhov, A. A. Trofimuk // Archiv der Mathematik. – 2021. – Vol. 116, № 3. – P. 241–249.