Let $G$ be a group and $A=Aut(G)$ be the group of automorphisms of $G$. Then the element $[g,\alpha]=g^{-1}\alpha(g)$ is an autocommutator of $g\in G$ and $\alpha\in A$. Also, the autocommutator subgroup of G is defined to be $K(G)=\langle[g,\alpha]|g\in G, \alpha\in A\rangle$, which is a characteristic subgroup of $G$ containing the derived subgroup $G'$ of $G$. A group is defined as A-perfect, if it equals its own autocommutator subgroup. The present research is aimed at classifying finite abelian groups which are A-perfect.
C. Chi$\check{s}$, M. Chi$\check{s}$, and G. Silberberg (2008). Abelian groups as
autocommutator groups. Arch. Math. (Basel).. 90 (6), 490-492 P. Hegarty (1994). The absolute centre of a group. J.
Algebra.. 169 (3), 929-935
Nasrabadi, M. M. and Gholamian, A. (2012). On finite A-perfect abelian groups. International Journal of Group Theory, 1(3), 11-14. doi: 10.22108/ijgt.2012.764
MLA
Nasrabadi, M. M. , and Gholamian, A. . "On finite A-perfect abelian groups", International Journal of Group Theory, 1, 3, 2012, 11-14. doi: 10.22108/ijgt.2012.764
HARVARD
Nasrabadi, M. M., Gholamian, A. (2012). 'On finite A-perfect abelian groups', International Journal of Group Theory, 1(3), pp. 11-14. doi: 10.22108/ijgt.2012.764
CHICAGO
M. M. Nasrabadi and A. Gholamian, "On finite A-perfect abelian groups," International Journal of Group Theory, 1 3 (2012): 11-14, doi: 10.22108/ijgt.2012.764
VANCOUVER
Nasrabadi, M. M., Gholamian, A. On finite A-perfect abelian groups. International Journal of Group Theory, 2012; 1(3): 11-14. doi: 10.22108/ijgt.2012.764
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