Abstract
We obtain a description of finite groups all of whose Schmidt subgroups are either supersolvable or not supersolvable. In particular, we show that these groups are always solvable.
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References
L. A. Shemetkov,Formations of Finite Groups [in Russian], “Nauka,” Moscow (1978).
J. Thompson, “Nonsolvable finite groups all of whose local subgroups are solvable,”Bull. Amer. Math. Soc.,74, No. 3, 383–437 (1968).
B. Huppert,Endliche Gruppen, Vol. I, Berlin (1967).
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Translated fromMatematicheskie Zametki, Vol. 58, No. 5, pp. 717–722, November, 1995.
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Monakhov, V.S. Finite groups with a given set of Schmidt subgroups. Math Notes 58, 1183–1186 (1995). https://doi.org/10.1007/BF02305002
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DOI: https://doi.org/10.1007/BF02305002