Finite Groups with Few TI-Subgroups

Shirong Li Department of Mathematics, Guangxi University, Nanning, Guangxi, P.R. China

Zhencai Shen Department of Mathematics of College of Science, China Agricultural University, Beijing, ChinaCorrespondence[email protected] [email protected]

Ni Du School of Mathematics Sciences, Xiamen University, Xiamen, Fujian, P.R. China

Abstract

A subgroup A of a finite group G is called a TI-subgroup if either A ∩ A ^x = 1 or A ∩ A ^x = A holds for all x ∈ G. In this paper, finite group all of whose meta-cyclic subgroups are TI-subgroups are classified completely. In particular, such groups are solvable.

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Notes

Communicated by V. A. Artamonov.

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Finite Groups with Few TI-Subgroups

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