Autocentralizer automorphisms of groups
محورهای موضوعی : Group theoryF. Karimi 1 , M. M. Nasrabadi 2 , A. Kaheni 3
1 - Department of Mathematics, Faculty of Mathematical Science and Statistics, University of Birjand, Birjand, Iran
2 - Department of Mathematics, Faculty of Mathematical Science and Statistics, University of Birjand, Birjand, Iran
3 - Department of Mathematics, Faculty of Mathematical Science and Statistics, University of Birjand, Birjand, Iran
کلید واژه: Centralizer subgroup, autocentralizer subgroup, autocentralizer automorphism,
چکیده مقاله :
Let $G$ be a group and $C_G(a)$ be a normal centralizer subgroup of $G$ for some $a\in G.$ Assume that, $\Upsilon^a _2(G)= [G, C_G(a)]$ and $Aut^{\Upsilon^a _2(G)}_{Z(C_G(a))}(G)$ is the set of all automorphisms of $G$ that centralizes $\frac {G}{\Upsilon ^a_2(G)}$ and $Z(C_G(a)).$ In this paper, we focus on the group $Aut^{\Upsilon^a _2(G)}_{Z(C_G(a))}(G)$ and try to characterize its properties.
Let $G$ be a group and $C_G(a)$ be a normal centralizer subgroup of $G$ for some $a\in G.$ Assume that, $\Upsilon^a _2(G)= [G, C_G(a)]$ and $Aut^{\Upsilon^a _2(G)}_{Z(C_G(a))}(G)$ is the set of all automorphisms of $G$ that centralizes $\frac {G}{\Upsilon ^a_2(G)}$ and $Z(C_G(a)).$ In this paper, we focus on the group $Aut^{\Upsilon^a _2(G)}_{Z(C_G(a))}(G)$ and try to characterize its properties.
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