Rendiconti del Seminario Matematico della Università di Padova

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Volume 131, 2014, pp. 77–87
DOI: 10.4171/RSMUP/131-6

Finite groups with some CAP-subgroups

Luis M. Ezquerro[1], Xianhua Li[2] and Yangming Li[3]

(1) Departamento de Matemáticas, Universidad Pública de Navarra, 31006, Pamplona, Spain
(2) Department of Mathematics, Suzhou University, 215006, Suzhou, China
(3) Department of Mathematics, Guangdong Institute of Education, 510310, Guangzhou, China

A subgroup $A$ of a group $G$ is said to be a CAP-subgroup of $G$ if for any chief factor $H/K$ of $G$, there holds $H\cap A = K\cap A$ or $HA = KA$. We investigate the influence of CAP-subgroups on the structure of finite groups. Some recent results are generalized.

Keywords: CAP-subgroup, the smallest generator number of a $p$-group, $p$-supersolvable group

Ezquerro Luis, Li Xianhua, Li Yangming: Finite groups with some CAP-subgroups. Rend. Sem. Mat. Univ. Padova 131 (2014), 77-87. doi: 10.4171/RSMUP/131-6