Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 70, No. 1, pp. 179-185, 2020

On TI-subgroups and QTI-subgroups of finite groups

Ruifang Chen, Xianhe Zhao

Received April 21, 2018. Published online September 16, 2019.

Abstract: 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 $C_G(x) \leq N_G(H)$ 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.

Keywords: TI-subgroup; QTI-subgroup; maximal subgroup; Frobenius group; solvable group

Classification MSC: 20D10

DOI: 10.21136/CMJ.2019.0203-18

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Ruifang Chen (corresponding author), Xianhe Zhao, School of Mathematics and Information Science, Henan Normal University, N. 46, East of Construction Road, Xinxiang, Henan, 453007, P. R. China, e-mail: fang119128@126.com, zhaoxianhe989@163.com

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