Finite p-Groups with Few Non-major k-Maximal Subgroups

Citation:

Boyan WEI,Haipeng QU,Yanfeng LUO.Finite p-Groups with Few Non-major k-Maximal Subgroups[J].Chinese Annals of Mathematics B,2018,39(1):59~68
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Authors:

Boyan WEI; Haipeng QU;Yanfeng LUO

Foundation:

This work was supported by the National Natural Science Foundation of China (Nos.11371232, 11371177).
Abstract: A subgroup of index $p^k$ of a finite $p$-group $G$ is called a $k$-maximal subgroup of $G$. Denote by $d(G)$ the number of elements in a minimal generator-system of $G$ and by $\delta_k(G)$ the number of $k$-maximal subgroups which do not contain the Frattini subgroup of $G$. In this paper, the authors classify the finite $p$-groups with $\delta_{d(G)}(G)\leq p^2$ and $\delta_{d(G)-1}(G)=0$, respectively.

Keywords:

Finite $p$-groups, $k$-Maximal subgroups, $k$-Major subgroups, Frattini subgroup, ,The number of non-major $k$-maximal subgroups

Classification:

20D15
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