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Inspired by this question Subgroups with trivial CentralizersSubgroups with trivial Centralizers, one can define a characteristic subgroup in any group $G$ as follows $$\Lambda(G)=\bigcap\{ H\leq G: C_G(H)=Z(G)\}$$ Is there any description of this subgroup in terms of known group theoretic objects?

Inspired by this question Subgroups with trivial Centralizers, one can define a characteristic subgroup in any group $G$ as follows $$\Lambda(G)=\bigcap\{ H\leq G: C_G(H)=Z(G)\}$$ Is there any description of this subgroup in terms of known group theoretic objects?

Inspired by this question Subgroups with trivial Centralizers, one can define a characteristic subgroup in any group $G$ as follows $$\Lambda(G)=\bigcap\{ H\leq G: C_G(H)=Z(G)\}$$ Is there any description of this subgroup in terms of known group theoretic objects?

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Sh.M1972
Sh.M1972
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Subgroups with minimal centralizers

Inspired by this question Subgroups with trivial Centralizers, one can define a characteristic subgroup in any group $G$ as follows $$\Lambda(G)=\bigcap\{ H\leq G: C_G(H)=Z(G)\}$$ Is there any description of this subgroup in terms of known group theoretic objects?