Author/Authors :
نقشينه، محمد نويسنده Islamic Azad University, Jahrom-Branch Naghshineh, Mohammad , مقدم، محمد رضا نويسنده Emeritus Professor, Faculty of Natural Resources, University of Tehran, Karaj, I.R. Iran Moghaddam, M. R. , پروانه، فرود نويسنده Islamic Azad University, Kermanshah-Branch Parvaneh, Foroud
Abstract :
Let G be a group and Aut(G) be the group of auto-
morphisms of G. Then [g; ®; ¯] = (g?1g®)?1(g?1g®)¯ is the au-
tocommutator of the element g 2 G and ®; ¯ 2 Aut(G) of weight
3. Also, we de¯ne K2(G) = < [g; ®; ¯] : g 2 G; ®; ¯ 2 Aut(G) >
to be the third term of the lower autocentral series of subgroups
of G. In this paper, it is shown that every ¯nite abelian group
is isomorphic to the third term of the autocentral series of some
¯nite abelian group.
