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J. Korean Math. Soc. 2009; 46(6): 1165-1178
Printed November 1, 2009
https://doi.org/10.4134/JKMS.2009.46.6.1165
Copyright © The Korean Mathematical Society.
Finite groups which have many normal subgroups
Qinhai Zhang, Xiaoqiang Guo, Haipeng Qu, and Mingyao Xu
Shanxi Normal University, Hebei Polytechnic University, Shanxi Normal University, and Shanxi Normal University
In this paper we classify finite groups whose nonnormal subgroups are of order $p$ or $pq$, where $p,\ q$ are primes. As a by-product, we also classify the finite groups in which all nonnormal subgroups are cyclic.
Keywords: finite $p$-groups, inner abelian $p$-groups, Dedekind groups, central product
MSC numbers: Primary 20D15; 20E99
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