Finite groups with H -embedded subgroups
Rendiconti del Seminario Matematico della Università di Padova, Tome 148 (2022), pp. 51-63.
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Let G be a finite soluble group and let 𝔉 be a class of groups. A chief factor H/K of G is said to be 𝔉-central (in G) if (H/K)(G/C G (H/K))𝔉; we write c𝔉 (G) to denote the set of all subgroups A of G such that every chief factor H/K of G between A G and A G is 𝔉-central in G. Let be a set of subgroups of G. We say that a subgroup A of G is H -embedded in G provided A is a Hall subgroup of some subgroup E. In this paper, we study the structure of G under the condition that every subgroup of G is H -embedded in G, where = c𝔉 (G) for some hereditary saturated formation 𝔉. Some known results are generalized.

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Publié le :
DOI : 10.4171/rsmup/102
Classification : 20
@article{RSMUP_2022__148__51_0,
     author = {Bin Hu and Jianhong Huang and Alexander N. Skiba},
     title = {Finite groups with $H_{\mathcal L}$-embedded subgroups},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {51--63},
     volume = {148},
     year = {2022},
     doi = {10.4171/rsmup/102},
     mrnumber = {4542372},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/rsmup/102/}
}
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Bin Hu; Jianhong Huang; Alexander N. Skiba. Finite groups with $H_{\mathcal L}$-embedded subgroups. Rendiconti del Seminario Matematico della Università di Padova, Tome 148 (2022), pp. 51-63. doi : 10.4171/rsmup/102. http://www.numdam.org/articles/10.4171/rsmup/102/

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