Rendiconti del Seminario Matematico della Università di Padova
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Finite groups with some CAP-subgroupsLuis M. Ezquerro, Xianhua Li and Yangming Li (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