Abstract
Normal subgroups of a group play an important role in determining the structure of a group. A Dedekindian group is the group all of whose subgoups are normal. The classification of such finite groups has been completed in 1897 by Dedekind. And Passman gave a classification of finite p-groups all of whose nonnormal subgroups are of order p. Above such two finite groups have many normal subgroups. Alone this line, to study the finite p-groups all of whose nonnormal subgroups are of order p or p 2, that is, its subgroups of order ≥ p 3 are normal. According to the order of the derived subgroups, divide into two cases expression and give all non-isomophic groups.
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Guo, X., Liu, Q., Zheng, S., Feng, L. (2010). Finite p-groups Which Have Many Normal Subgroups. In: Zhu, R., Zhang, Y., Liu, B., Liu, C. (eds) Information Computing and Applications. ICICA 2010. Communications in Computer and Information Science, vol 105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16336-4_64
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DOI: https://doi.org/10.1007/978-3-642-16336-4_64
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