THE LOWER AUTOCENTRAL SERIES OF ABELIAN GROUPS

Title & Authors
THE LOWER AUTOCENTRAL SERIES OF ABELIAN GROUPS

Abstract
In the present paper we introduce the lower autocentral series of autocommutator subgroups of a given group. Following our previous work on the subject in 2009, it is shown that every finite abelian group is isomorphic with $\small{n^{th}}$-term of the lower autocentral series of some finite abelian group.
Keywords
autocommutator subgroup;autocentral series;abelian group;
Language
English
Cited by
1.
AUTOCOMMUTATORS AND AUTO-BELL GROUPS,;;;

대한수학회보, 2014. vol.51. 4, pp.923-931
2.
NON-ABELIAN TENSOR ANALOGUES OF 2-AUTO ENGEL GROUPS,;;

대한수학회보, 2015. vol.52. 4, pp.1097-1105
1.
Autonilpotent groups and their properties, Asian-European Journal of Mathematics, 2016, 09, 03, 1650056
2.
NON-ABELIAN TENSOR ANALOGUES OF 2-AUTO ENGEL GROUPS, Bulletin of the Korean Mathematical Society, 2015, 52, 4, 1097
3.
AUTOCOMMUTATORS AND AUTO-BELL GROUPS, Bulletin of the Korean Mathematical Society, 2014, 51, 4, 923
4.
Relative autocommutator subgroups of abelian groups, Journal of Algebra and Its Applications, 2017, 16, 05, 1750086
5.
On A-nilpotent abelian groups, Proceedings - Mathematical Sciences, 2014, 124, 4, 517
References
1.
C. Chis, M. Chis, and G. Silberberg, Abelian groups as autocommutator groups, Arch. Math. (Basel) 90 (2008), no. 6, 490-492.

2.
M. Deaconescu and G. L.Walls, Cyclic groups as autocommutator groups, Comm. Algebra 35 (2007), no. 1, 215-219.

3.
P. Hegarty, The absolute centre of a group, J. Algebra 169 (1994), no. 3, 929-935.

4.
P. Hegarty, Autocommutator subgroups of finite groups, J. Algebra 190 (1997), no. 2, 556-562.

5.
M. Naghshineh, M. R. R. Moghaddam, and F. Parvaneh, The third term of the lower autocentral series of abelian groups, Journal of Mathematical Extension, Vol. 4, No. 1 (2009), 1-6.

6.
D. J. S. Robinson, A Course in the Theory of Groups, Graduate Texts in Mathematics, 80. Springer-Verlag, New York-Berlin, 1982.