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On TI-subgroups and QTI-subgroups of finite groups
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 1, pp. 179-185
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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.
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.
DOI : 10.21136/CMJ.2019.0203-18
Classification : 20D10
Keywords: TI-subgroup; QTI-subgroup; maximal subgroup; Frobenius group; solvable group 
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Chen, Ruifang; Zhao, Xianhe. On TI-subgroups and QTI-subgroups of finite groups. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 1, pp. 179-185. doi: 10.21136/CMJ.2019.0203-18

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