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Lee Mosher
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make the body self-contained, make title less prone to misreading
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Arturo Magidin
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Can one characterize amenable groups with the following property:$C_G(x)$ cyclic for all $x\neq 1$?

Can one characterize the amenable groups that have the property that the centralizer of every non-identity element is cyclic. For?

For example, must they be solvable?

Can one characterize amenable groups with the following property:

the centralizer of every non-identity element is cyclic. For example, must they be solvable?

Can one characterize amenable groups with $C_G(x)$ cyclic for all $x\neq 1$?

Can one characterize the amenable groups that have the property that the centralizer of every non-identity element is cyclic?

For example, must they be solvable?

Proper tag.
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Stefan Kohl
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