Finite Groups With Maximal Normalizers I

2009/05/23 by Joseph P. Bohanon, Joseph Bohanon, Bohanon, Joseph
Computer Science · Engineering · Mathematics · #20D15 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems #math.GR #msc:20D15

paper · pdf · doi:10.48550/arxiv.0905.3790

16 pages. An example is included and some more exposition. No major corrections were made

openalex publication_date 2009/05/23 · arxiv created 2009/06/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We examine p-groups with the property that every non-normal subgroup has a normalizer which is a maximal subgroup. In particular we show that for such a p-group G, when p=2, the center of G has index at most 16 and when p is odd the center of G has index at most p³.

Related

• Finite groups with many normalizers
• Some restrictions on normalizers or centralizers in finite p-groups
• The class MN of groups in which all maximal subgroups are normal
• Finite groups with Frobenius normalizer condition for non-normal primary subgroups
• Classification of Maximal Subgroups of Odd Index in Finite Simple Classical groups: Addendum