# NOMALIZERS OF NONNORMAL SUBGROUPS OF FINITE p-GROUPS

• Zhang, Qinhai ;
• Gao, Juan
• Published : 2012.01.01
• 55 6

#### Abstract

Assume G is a finite p-group and i is a fixed positive integer. In this paper, finite p-groups G with ${\mid}N_G(H):H{\mid}=p^i$ 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

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#### Cited by

1. Some restrictions on normalizers or centralizers in finite p-groups vol.208, pp.1, 2015, https://doi.org/10.1007/s11856-015-1197-1
2. Some finiteness conditions on normalizers or centralizers in groups 2017, https://doi.org/10.1080/00927872.2017.1363223
3. Finite $$p$$ p -Groups all of Whose Nonnormal Subgroups Posses Special Normalizers vol.40, pp.1, 2017, https://doi.org/10.1007/s40840-016-0322-6
4. A finiteness condition on centralizers in locally nilpotent groups vol.182, pp.2, 2017, https://doi.org/10.1007/s00605-015-0854-0

#### Acknowledgement

Supported by : NSFC, NSF of Shanxi Province