Finite Solvable Groups in Which the -Quasinormality of Subgroups is a Transitive Relation

Let be a partition of the set of all primes, and let be a finite group. The group is said to be -primary if is a -group for some and -complete if has a Hall -subgroup for each . A subgroup of is (i) -subnormal in if it has a subgroup series such that either or is -primary for each ; (ii) modular in...

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Bibliographic Details
Published inMathematical Notes Vol. 114; no. 5-6; pp. 1021 - 1028
Main Authors Wang, Zhigang, Guo, Wenbin, Safonova, I. N., Skiba, A. N.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 2023
Springer Nature B.V
Subjects
14/34
639/766/189
639/766/530
639/766/747
Group theory
Mathematics
Mathematics and Statistics
Subgroups
finite group
solvable group
quasinormal subgroup
modular subgroup
group
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Summary:Let be a partition of the set of all primes, and let be a finite group. The group is said to be -primary if is a -group for some and -complete if has a Hall -subgroup for each . A subgroup of is (i) -subnormal in if it has a subgroup series such that either or is -primary for each ; (ii) modular in if (1) for all such that and (2) for all such that ; (iii) -quasinormal in if is -subnormal and modular in . Finite solvable groups in which the -quasinormality of subgroups is a transitive relation are described. Some known results are generalized.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434623110330