A remark on a product of two formational tcc-subgroups
https://doi.org/10.22405/2226-8383-2021-22-1-495-501
Abstract
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 6 𝐴 and 𝑌 6 𝑇 there exists an element 𝑢 ∈ ⟨𝑋, 𝑌 ⟩ such that 𝑋𝑌 𝑢 ≤ 𝐺. The notation 𝐻 6 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 such that U ⊆ F. Here U is the formation of all supersoluble groups.
About the Author
Alexander Alexandrovich Trofimuk
Brest State A.S. Pushkin University
Belarus
Belarus
candidate of physical and mathematical sciences
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Review
For citations:
Trofimuk A.A. A remark on a product of two formational tcc-subgroups. Chebyshevskii Sbornik. 2021;22(1):495-501. (In Russ.) https://doi.org/10.22405/2226-8383-2021-22-1-495-501
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