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On a product of two formational tcc-subgroups
Репозиторій DSpace/Manakin
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On a product of two formational tcc-subgroups
Інший ID:
DOI:10.12958/adm1396
2010 MSC: 20D10.
2010 MSC: 20D10.
Посилання:
On a product of two formational tcc-subgroups / A. Trofimuk // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 2. — С. 282–289. — Бібліогр.: 15 назв. — англ.
Підтримка:
For the 70th anniversary of L. A. Kurdachenko. This work was supported by the BRFFR (grant No. F19RM-071).
Дата:
2020
Переглядів:
243
Завантажень:
132
Анотація:
A subgroup A of a group G is called tcc-subgroup in G, if there is a subgroup T of G such that G = AT and for any X ≤ A and Y ≤ T there exists an element u ∈ hX, Y i such that XYᵘ ≤ G. The notation H ≤ G means that H is a subgroup of a group G. In this paper we consider a group G = AB such that A and B are tcc-subgroups in G. We prove that G belongs to F, when A and B belong to F and F is a saturated formation of soluble groups such that U ⊆ F. Here U is the formation of all supersoluble groups.
