Abstract
Under study is the structure of a finite non-\( r \)-nilpotent group, with \( r\in\{2,3,5\} \), in which any non-\( r \)-nilpotent maximal subgroup is a \( \Phi \)-simple group.
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Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 1, pp. 23–41. https://doi.org/10.33048/smzh.2022.63.102
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Bazhanova, E.N., Vedernikov, V.A. Finite Groups with \( p \)-Nilpotent or \( \Phi \)-Simple Maximal Subgroups. Sib Math J 63, 19–33 (2022). https://doi.org/10.1134/S0037446622010025
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DOI: https://doi.org/10.1134/S0037446622010025
Keywords
- maximal subgroup
- \( pd \)-group
- \( p \)-decomposable group
- \( p \)-closed group
- \( p \)-nilpotent group
- \( p \)-solvable group
- \( \Phi \)-simple group
- Schmidt group
- Frattini subgroup