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| Finite p-Groups with Few Non-major k-Maximal Subgroups |
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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 |
| Page view： 2127
Net amount： 1771 |
Authors： |
Boyan WEI; Haipeng QU;Yanfeng LUO |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11371232, 11371177). |
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| 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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