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edit approved Apr 13, 2017 at 15:04
maryam
edit approved Apr 13, 2017 at 15:04
maryam
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I am interested in the nonabelian finite $p$-group $G$ with the following property:

$G$ has a maximal abelian subgroup $A$ and there exists an $x\in G\setminus A$ such that $x$ normalize $A$ but $x$ does not commute with any noncentral element of $A$.

$p$-groups with maximal class have this property since they have maximal abelian subgroup of order $p^2$. Any reference or comment or maybe partial characterization will be useful for me.

I am interested in the nonabelian finite $p$-group $G$ with the following property:

$G$ has a maximal abelian subgroup $A$ and $x\in G\setminus A$ such that $x$ normalize $A$ but $x$ does not commute with any noncentral element of $A$.

$p$-groups with maximal class have this property since they have maximal abelian subgroup of order $p^2$. Any reference or comment or maybe partial characterization will be useful for me.

I am interested in the nonabelian finite $p$-group $G$ with the following property:

$G$ has a maximal abelian subgroup $A$ and there exists an $x\in G\setminus A$ such that $x$ normalize $A$ but $x$ does not commute with any noncentral element of $A$.

$p$-groups with maximal class have this property since they have maximal abelian subgroup of order $p^2$. Any reference or comment or maybe partial characterization will be useful for me.

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Maryam
Maryam
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a p-group with special property on one maximal abelian subgroup

I am interested in the nonabelian finite $p$-group $G$ with the following property:

$G$ has a maximal abelian subgroup $A$ and $x\in G\setminus A$ such that $x$ normalize $A$ but $x$ does not commute with any noncentral element of $A$.

$p$-groups with maximal class have this property since they have maximal abelian subgroup of order $p^2$. Any reference or comment or maybe partial characterization will be useful for me.