On some product of SM-groups
https://doi.org/10.22405/2226-8383-2024-25-1-170-175
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 ⩽ 𝐴 and 𝑌 ⩽ 𝑇 there exists an element 𝑢 ∈ ⟨𝑋, 𝑌 ⟩ such that 𝑋𝑌^𝑢 ≤ 𝐺. The notation 𝐻 ⩽ 𝐺 means that 𝐻 is a subgroup of a group 𝐺. In this paper we proved that the class of all SM-groups is closed under the product of tcc- subgroups. Here an SM-group is a group where each subnormal subgroup permutes with every maximal subgroup.
About the Authors
Dmitry Vladimirovich Gritsuk
A. S. Pushkin Brest State University
Belarus
Belarus
candidate of physical and mathematical sciences
Alexander Aleksandrovich Trofimuk
A. S. Pushkin Brest State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences
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Review
For citations:
Gritsuk D.V., Trofimuk A.A. On some product of SM-groups. Chebyshevskii Sbornik. 2024;25(1):170-175. (In Russ.) https://doi.org/10.22405/2226-8383-2024-25-1-170-175
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