Co-prolongations of a group extension

Document Type : Research Paper


1 Hanoi National University of Education

2 National Economics University

3 Hanoi University of Science and Technology


The aim of this paper is to study co-prolongations‎ ‎of central extensions‎. ‎We construct the obstruction theory for‎ ‎co-prolongations‎ ‎and classify the equivalence classes of these by kernels of homomorphisms‎ ‎between 2-dimensional cohomology groups of groups‎.


Main Subjects

K. S. Brown (1982). Cohomology of groups. Springe-Verlag, New York-Berlin. Springe-Verlag, New York-Berlin (1994). Covering groups of nonconnected topological groups revisited. Math. Proc. Cambridge Philos. Soc.. 115 (1), 97-110 P. Hilton (1971). Lectures in homological algebra. Amer. Math. Soc.. (8) S. Mac Lane (1985). Extensions and obstruction for rings. Illinois J. Math.. 2, 316-345 S. Mac Lane (1963). Homology (Die Grundlehren der mathematischen Wissenschaften). Bd. 114 Academic Press, Inc., Publishers, New York, Springer-Verlag, Berlin-Göttingen-Heidelberg. S. Mac Lane (1988). Group extensions for 45 years. Math. Intelligencer. 10 (2), 29-35 G. K. Pedersen (1999). Pullback and pushout constructions in $C\sp *$-algebra theory. J. Funct. Anal.. 167 (2), 243-344 N. T. Quang, C. T. Kim Phung and P. Thi Cuc (2012). The prolongation of central extensions. Int. J. Group Theory. 1 (2), 39-49 E. Weiss (1969). Cohomology of groups. Pure and Applied Mathematics, Academic Press, New York-London. 34 J. H. C. Whitehead (1949). Combinatorial homotopy II. Bull. Amer. Math. Soc.. 55, 453-496
  • Receive Date: 25 February 2013
  • Revise Date: 18 August 2013
  • Accept Date: 18 August 2013
  • Published Online: 01 March 2014