Finite Groups With Maximal Normalizers I

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Bohanon, Joseph
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Abstract
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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 $p^3$.
Comment: 16 pages. An example is included and some more exposition. No major corrections were made
Keywords
Mathematics - Group Theory, 20D15
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