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On finite A-perfect abelian groups | ||
| International Journal of Group Theory | ||
| مقاله 2، دوره 1، شماره 3، آذر 2012، صفحه 11-14 اصل مقاله (362.44 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2012.764 | ||
| نویسندگان | ||
| Mohammad Mehdi Nasrabadi* 1؛ Ali Gholamian2 | ||
| 1Department of Maths,birjand university | ||
| 2Department of mathematics, Birjand university, Birjand | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Automorphism؛ Autocommutator subgroup؛ A-perfect group؛ Finite abelian group | ||
| مراجع | ||
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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
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