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Keywords:
TI-subgroup; QTI-subgroup; maximal subgroup; Frobenius group; solvable group
TI-subgroup; QTI-subgroup; maximal subgroup; Frobenius group; solvable group
Summary:
Let $G$ be a group. A subgroup $H$ of $G$ is called a TI-subgroup if $H\cap H^g=1$ or $H$ for every $g\in G$ and $H$ is called a QTI-subgroup if $C_G(x) \le N_G(H)$ for any $1\neq x\in H$. In this paper, a finite group in which every nonabelian maximal is a TI-subgroup (QTI-subgroup) is characterized.
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