Frontiers of Mathematics in China >
Finite 2-groups whose nonnormal subgroups have orders at most 23
Received date: 03 Mar 2012
Accepted date: 17 Apr 2012
Published date: 01 Oct 2012
Copyright
In this paper, we classify finite 2-groups all of whose nonnormal subgroups have orders at most 23. Together with a known result, we completely solved Problem 2279 proposed by Y. Berkovich and Z. Janko in Groups of Prime Power Order, Vol. 3.
Qinhai ZHANG , Meijuan SU . Finite 2-groups whose nonnormal subgroups have orders at most 23[J]. Frontiers of Mathematics in China, 2012 , 7(5) : 971 -1003 . DOI: 10.1007/s11464-012-0216-3
1 |
Berkovich Y. Groups of Prime Power Order, Vol. 1. Berlin, New York: Walter de Gruyter, 2008
|
2 |
Berkovich Y, Janko Z. Groups of Prime Power Order, Vol. 2. Berlin, New York: Walter de Gruyter, 2008
|
3 |
Berkovich Y, Janko Z. Groups of Prime Power Order, Vol. 3. Berlin, New York: Walter de Gruyter, 2011
|
4 |
Huppert B. Endliche Gruppen I. Berlin, Heidelberg, New York: Springer-Verlag, 1967
|
5 |
Passman D S. Nonnormal subgroups of p-groups. J Algebra, 1970, 15: 352-370
|
6 |
Zhang G H, Guo X Q, Qu H P, Xu M Y. Finite group which have many normal subgroups. J Korean Math Soc, 2009, 46(6): 1165-1178
|
7 |
Zhang Q H, Li X X, Su M J. Finite p-groups whose nonnormal subgroups have orders≤p3 (in preparation)
|
8 |
Zhang Q H, Sun X J, An L J, Xu M Y. Finite p-groups all of whose subgroups of index p2 are abelian. Algebra Colloq, 2008, 15(1): 167-180
|
/
〈 | 〉 |