Finite solvable groups with a nilpotent normal complement subgroup

Mohsen Amiri

Finite solvable groups with a nilpotent normal complement subgroup

Group Theory 2023-11-20 v6

Authors: Mohsen Amiri

Abstract

Let $G$ be a finite solvable group and $H$ a non-normal core-free subgroup of $G$ . We show that if the normalizer of any non-trivial normal subgroup of $Fit(H)$ is equal $H$ , then $H$ has a nilpotent normal complement $K$ such that $G=KH$ and $KZ(Fit(H))$ is a Frobenius group.

Keywords

finite group theory

Cite

@article{arxiv.2112.14992,
  title  = {Finite solvable groups with a nilpotent normal complement subgroup},
  author = {Mohsen Amiri},
  journal= {arXiv preprint arXiv:2112.14992},
  year   = {2023}
}

Comments

The accepted version of the paper

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