Finite Groups with Systems of Σ- $$\mathfrak{F}$$ F -Embedded Subgroups

Yuemei Mao () and Xiaojian Ma ()
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Yuemei Mao: Shanxi Datong University
Xiaojian Ma: University of Datong of Shanxi

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 3, 901-914

Abstract: Abstract Let $$\mathfrak{F}$$ F denote a class of groups. A maximal subgroup M of G is called $$\mathfrak{F}$$ F -abnormal provided G/MG ∉ $$\mathfrak{F}$$ F . We say that (K, H) is an $$\mathfrak{F}$$ F -abnormal pair of G provided K is a maximal $$\mathfrak{F}$$ F -abnormal subgroup of H. Let Σ = {G0 ≤ G1 ≤ G2 ≤ … ≤ Gn} be a subgroup series of G. A subgroup H of G is said to be Σ- $$\mathfrak{F}$$ F -embedded in G if H either covers or avoids every $$\mathfrak{F}$$ F -abnormal pair (K, H) such that Gi−1≤ K

Keywords: Finite group; $$\mathfrak{F}$$ F -abnormal pair; Σ- $$\mathfrak{F}$$ F -embedded; p-supersoluble groups; p-soluble groups; 20D10; 20D20; 20D35 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0440-6

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