| Finite $p$-Groups with Large or Small Normal Closures of Non-Normal Cyclic Subgroups |
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| Key Words:
$JC$-group non-Dedekindian $p$-group regular $p$-group
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11526114; 11601245), the Natural Science Foundation of Guangdong Province (Grant No.2015A030313791), the Innovative Team Project of Guangdong Province (CHINA) (Grant No.2014KTSCX196), Guangdong Province Innovation Talent Project for Youths (Grant No.2015KQNCX107) and the Appropriative Researching Fund for Doctors, Guangdong University of Education (Grant No.2013ARF07). |
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| Abstract: |
| A $p$-group $G$ is called a $JC$-group if the normal closure $H^G$ of every cyclic subgroup $H$ satisfies $|G:H^G|\leq p$ or $|H^G:H|\leq p$. In this paper, we classify the non-Dedekindian $JC$-groups for $p>2$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2017.02.009 |
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