A characterization of finite σ-soluble PσT-groups
Rendiconti del Seminario Matematico della Università di Padova, Tome 148 (2022), pp. 203-212.
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Let 𝔉 be a non-empty class of groups, G a finite group and (G) be the lattice of all subgroups of G. A chief factor H/K of G is 𝔉-central in G if (H/K)(G/C G (H/K))𝔉. Let c𝔉 (G) be the set of subgroups A of G such that every chief factor of G between A G and A G is 𝔉-central in G; let 𝔉 (G) be the set of subgroups A of G such that A G /A G 𝔉. In this paper, we study the influence of 𝔉 (G) and c𝔉 (G) on the structure of G, where 𝔉 is a normally hereditary saturated formation containing all σ-nilpotent groups and D=G 𝔉 is σ-soluble. Moreover, we give a new characterization of a finite σ-soluble group to be a PσT-group.

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DOI : 10.4171/rsmup/108
Classification : 20
@article{RSMUP_2022__148__203_0,
     author = {Chenchen Cao and Dein Wong and Chi Zhang},
     title = {A characterization of finite $\sigma$-soluble $P\sigma T$-groups},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {203--212},
     volume = {148},
     year = {2022},
     doi = {10.4171/rsmup/108},
     mrnumber = {4542378},
     zbl = {1511.20064},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/rsmup/108/}
}
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Chenchen Cao; Dein Wong; Chi Zhang. A characterization of finite $\sigma$-soluble $P\sigma T$-groups. Rendiconti del Seminario Matematico della Università di Padova, Tome 148 (2022), pp. 203-212. doi : 10.4171/rsmup/108. http://www.numdam.org/articles/10.4171/rsmup/108/

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