JOURNAL BROWSE
Search
Advanced SearchSearch Tips
NOMALIZERS OF NONNORMAL SUBGROUPS OF FINITE p-GROUPS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
NOMALIZERS OF NONNORMAL SUBGROUPS OF FINITE p-GROUPS
Zhang, Qinhai; Gao, Juan;
  PDF(new window)
 Abstract
Assume G is a finite p-group and i is a fixed positive integer. In this paper, finite p-groups G with for all nonnormal subgroups H are classified up to isomorphism. As a corollary, this answer Problem 116(i) proposed by Y. Berkovich in his book "Groups of Prime Power Order Vol. I" in 2008.
 Keywords
finite p-groups;nonnormal subgroups;self-normalizer;central extensions;
 Language
English
 Cited by
1.
Some restrictions on normalizers or centralizers in finite p-groups, Israel Journal of Mathematics, 2015, 208, 1, 193  crossref(new windwow)
2.
Finite $$p$$ p -Groups all of Whose Nonnormal Subgroups Posses Special Normalizers, Bulletin of the Malaysian Mathematical Sciences Society, 2016  crossref(new windwow)
3.
A finiteness condition on centralizers in locally nilpotent groups, Monatshefte für Mathematik, 2015  crossref(new windwow)
 References
1.
L. J. An, A classification of nite meta-Hamilton p-groups, Ph. D. dissertation, Beijing University, 2009.

2.
Y. Berkovich, Groups of Prime Power Order. Vol. 1, With a foreword by Zvonimir Janko. de Gruyter Expositions in Mathematics, 46. Walter de Gruyter GmbH & Co. KG, Berlin, 2008.

3.
R. W. Carter, Nilpotent self-normalizing subgroups of soluble groups, Math. Z. 75 (1960/1961), 136-139. crossref(new window)

4.
A. Fattahi, Groups with only normal and abnormal subgroups, J. Algebra 28 (1974), 15-19. crossref(new window)

5.
B. Huppert, Endliche Gruppen I, Spriger-Verlag, Berlin, Heidelberg, New York, 1967.

6.
L. L. Li, H. P. Qu, and G. Y. Chen, Central extension of inner abelian pp-groups. I, Acta Math. Sinica (Chin. Ser.) 53 (2010), no. 4, 675-684.

7.
D. S. Passman, Nonnormal subgroups of p-groups, J. Algebra 15 (1970), 352-370. crossref(new window)

8.
L. Redei, Das schiefe Product in der Gruppentheorie, Comment. Math. Helv. 20 (1947), 225-267. crossref(new window)

9.
M. Y. Xu, A theorem on metabelian p-groups and some consequences, Chin. Ann. Math. Ser. B 5 (1984), no. 1, 1-6.

10.
M. Y. Xu and H. P. Qu, Finite p-Groups, Beijing University Press, Beijing, 2010.

11.
Q. H. Zhang and J. X. Wang, Finite groups with quasi-normal and self-normalizer subgroups, Acta Math. Sinica (Chin. Ser.) 38 (1995), no. 3, 381-385.

12.
Q. H. Zhang, Finite groups with only seminormal and abnormal subgroups, J. Math. Study 29 (1996), no. 4, 10-15.

13.
Q. H. Zhang, Finite groups with only ss-quasinormal and abnormal subgroups, Northeast. Math. J. 14 (1998), no. 1, 41-46.

14.
Q. H. Zhang, s-semipermutability and abnormality in finite groups, Comm. Algebra 27 (1999), no. 9, 4515-4524. crossref(new window)

15.
Q. H. Zhang, X. Q. Guo, H. P. Qu, and M. Y. Xu, Finite groups which have many normal subgroups, J. Korean Math. Soc. 46 (2009), no. 6, 1165-1178. crossref(new window)