# On central endomorphisms of a group

Document Type: Ischia Group Theory 2014

Author

Seconda Universita di Napoli

Abstract

Let $\Gamma$ be a normal subgroup of the full automorphism group $Aut(G)$ of a group $G$‎, ‎and assume that $Inn(G)\leq \Gamma$‎. ‎An endomorphism $\sigma$ of $G$ is said to be $\Gamma$-central if $\sigma$ induces the the identity on the factor group $G/C_G(\Gamma)$‎. ‎Clearly‎, ‎if $\Gamma=Inn(G)$‎, ‎then a $\Gamma$-central endomorphism is a central endomorphism‎. ‎In this article the conditions under which a $\Gamma$-central endomorphism of a group is an automorphism are investigated‎.

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### References

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