## Abstract

Let π be a set of primes. According to H. Wielandt, a subgroup H of a finite group X is called a π-submaximal subgroup if there is a monomorphism ϕ: X→ Y into a finite group Y such that X^{ϕ} is subnormal in Y and H^{ϕ}= K∩ X^{ϕ} for a π-maximal subgroup K of Y. In his talk at the celebrated conference on finite groups in Santa-Cruz (USA) in 1979, Wielandt posed a series of open questions and among them the following problem: to describe the π-submaximal subgroup of the minimal nonsolvable groups and to study properties of such subgroups: the pronormality, the intravariancy, the conjugacy in the automorphism group etc. In the article, for every set π of primes, we obtain a description of the π-submaximal subgroup in minimal nonsolvable groups and investigate their properties, so we give a solution of Wielandt’s problem.

Original language | English |
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Pages (from-to) | 325-351 |

Number of pages | 27 |

Journal | Bulletin of Mathematical Sciences |

Volume | 8 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Aug 2018 |

## Keywords

- Minimal nonsolvable group
- Minimal simple group
- Pronormal subgroup
- π-Maximal subgroup
- π-Submaximal subgroup
- FINITE SIMPLE-GROUPS
- EXISTENCE
- pi-Maximal subgroup
- THEOREM
- CONJECTURE
- SYLOW TYPE
- HALL SUBGROUPS
- PRONORMALITY
- CRITERION
- pi-Submaximal subgroup