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FINITE GROUPS ALL OF WHOSE SECOND MAXIMAL SUBGROUPS ARE PSC-GROUPS

ZHENCAI SHEN

School of Mathematics, Suzhou University, Suzhou, Jiangsu, 215006, P. R. China

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SHIRONG LI

Department of Mathematics, Guangxi University, Nanning, Guangxi, 530004, P. R. China

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, and

WUJIE SHI

School of Mathematics, Suzhou University, Suzhou, Jiangsu, 215006, P. R. China

Corresponding author.

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https://doi.org/10.1142/S0219498809003291Cited by:3 (Source: Crossref)

Abstract

A subgroup H of G is said to be self-conjugate-permutable if HH^x = H^xH implies H^x = H. A finite group G is called PSC-group if every cyclic subgroup of group G of prime order or order 4 is self-conjugate-permutable. In the paper, first we give the structure of finite group G, all of whose maximal subgroups are PSC-groups. Then we also classified that finite group G all of whose second maximal subgroups are PSC-groups.

The project is supported in part by the Natural Science Foundation of China (No. 10161001) and the NNSF of China (No. 10871032).

Keywords:

AMSC: 20D10, 20D20

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