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NOMALIZERS OF NONNORMAL SUBGROUPS OF FINITE p-GROUPS

Juan Gao|Qinhai Zhang
대한수학회 (The Korean Mathematical Society)|2012.01|대한수학회지 (Journal of the KMS)|제49권 제1호|pp. 201-221

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키워드

finite p-groupsnonnormal subgroupsself-normalizercentral extensions
주제분류수학

초록

Assume G is a finite p-group and i is a fixed positive integer. In this paper, finite p-groups G with jNG(H) : Hj = pi for all nonnormal subgroups H are classified up to isomorphism. As a corollary, this answers Problem 116(i) proposed by Y. Berkovich in his book "Groups of Prime Power Order Vol. I" in 2008.

Abstract

Assume G is a finite p-group and i is a fixed positive integer. In this paper, finite p-groups G with jNG(H) : Hj = pi for all nonnormal subgroups H are classified up to isomorphism. As a corollary, this answers Problem 116(i) proposed by Y. Berkovich in his book "Groups of Prime Power Order Vol. I" in 2008.

참고문헌 (15)

  1. L. J. An, "A classification of finite meta-Hamilton p-groups", 박사, pp.2009
  2. Y. Berkovich, "Groups of Prime Power Order. Vol. 1, In de Gruyter Expositions in Mathematics, 46" (2008), Walter de Gruyter GmbH & Co. KG
  3. R. W. Carter, "Nilpotent self-normalizing subgroups of soluble groups", Math. Z, 75, pp.136~139 (1961)
  4. A. Fattahi, "Groups with only normal and abnormal subgroups", J. Algebra, 28, pp.15~19 (1974)
  5. B. Huppert, "Endliche Gruppen I" (1967), Spriger-Verlag
  6. L. L. Li, "Central extension of inner abelian pp-groups. I", Acta Math. Sinica (Chin. Ser.), 53(4), pp.675~684 (2010)
  7. D. S. Passman, "Nonnormal subgroups of p-groups", J. Algebra, 15, pp.352~370 (1970)
  8. L. Redei, "Das schiefe Product in der Gruppentheorie", Comment. Math. Helv, 20, pp.225~267 (1947)
  9. M. Y. Xu, "A theorem on metabelian p-groups and some consequences", Chin. Ann. Math. Ser. B, 5(1), pp.1~6 (1984)
  10. M. Y. Xu, "Finite p-Groups" (2010), Beijing University Press
  11. Q. H. Zhang, "Finite groups with quasi-normal and self-normalizer subgroups", Acta Math. Sinica (Chin. Ser.), 38(3), pp.381~385 (1995)
  12. Q. H. Zhang, "Finite groups with only seminormal and abnormal subgroups", J. Math. Study, 29(4), pp.10~15 (1996)
  13. Q. H. Zhang, "Finite groups with only ss-quasinormal and abnormal subgroups, Northeast", Math. J, (1), pp.41~46 (1998)
  14. Q. H. Zhang, "s-semipermutability and abnormality in finite groups", Comm. Algebra, 27(9), pp.4515~4524 (1999)
  15. Qinhai Zhang, "Finite groups which have many normal subgroups", 대한수학회지, 46(6), pp.1165~1178 (2009), 대한수학회

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