|
|
| |
| Finite p-Groups in Which the Number of Subgroups of Possible Order is Less Than or Equal to $p^3 $ |
| |
Citation： |
Haipeng QU,Ying SUN,Qinhai ZHANG.Finite p-Groups in Which the Number of Subgroups of Possible Order is Less Than or Equal to $p^3 $[J].Chinese Annals of Mathematics B,2010,31(4):497~506 |
| Page view： 1800
Net amount： 1669 |
Authors： |
Haipeng QU; Ying SUN; Qinhai ZHANG; |
Foundation： |
the National Natural Science Foundation of China (No. 10671114), the Shanxi
Provincial Natural Science Foundation of China (No. 2008012001) and the Returned Abroad-Student
Fund of Shanxi Province (No. [2007]13–56). |
|
|
| Abstract： |
In this paper, groups of order $p^n$ in which the number of
subgroups of possible order is less than or equal to $p^3 $ are
classified. It turns out that if $p>2,\ n\geq 5$, then the
classification of groups of order $p^n$ in which the number of
subgroups of possible order is less than or equal to $p^3 $ and the
classification of groups of order $p^n$ with a cyclic subgroup of
index $p^2$ are the same. |
Keywords： |
Inner abelian $p$-groups, Metacyclic $p$-groups, Groups of order
$p^n$ with a cyclic subgroup of index $p^2$, The number of subgroups |
Classification： |
20D15 |
|
|
Download PDF Full-Text
|
