The aim of this paper is to study the $(\alpha, \gamma)$-prolongation of central extensions. We obtain the obstruction theory for $(\alpha, \gamma)$-prolongations and classify $(\alpha, \gamma)$-prolongations thanks to low-dimensional cohomology groups of groups.
R. Brown and O. Mucuk (1994). Covering groups of nonconnected topological
groups revisited. Math. Proc. Cambridge Philos. Soc.. 115 (1), 97-110 C. Cotter and I. Szczyrba (1993). On realizations of
representations for group extensions. Rep. Math. Phys.. 32 (3), 355-366 G. Hochschild and J.-P. Serre (1953). Cohomology of group extensions. Trans. Amer. Math.
Soc.. 74, 110-134 S. Mac Lane (1988). Group extensions for 45 years. Math. Intelligencer. 10 (2), 29-35 S. Mac Lane (1963). Homology. Springer-Verlag, New York. G. K. Pedersen (1999). Pullback and pushout constructions in
$C\sp *$-algebra theory. 167 (2), 243-344 H. Sahleh (2007). On the pull-back of metabelian topological
groups. Int. J. Contemp. Math. Sci.. 2 (26), 1271-1278 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
Tien Quang, N. , Phung, C. T. K. and Cuc, P. T. (2012). The prolongation of central extensions. International Journal of Group Theory, 1(2), 39-49. doi: 10.22108/ijgt.2012.740
MLA
Tien Quang, N. , , Phung, C. T. K. , and Cuc, P. T. . "The prolongation of central extensions", International Journal of Group Theory, 1, 2, 2012, 39-49. doi: 10.22108/ijgt.2012.740
HARVARD
Tien Quang, N., Phung, C. T. K., Cuc, P. T. (2012). 'The prolongation of central extensions', International Journal of Group Theory, 1(2), pp. 39-49. doi: 10.22108/ijgt.2012.740
CHICAGO
N. Tien Quang , C. T. K. Phung and P. T. Cuc, "The prolongation of central extensions," International Journal of Group Theory, 1 2 (2012): 39-49, doi: 10.22108/ijgt.2012.740
VANCOUVER
Tien Quang, N., Phung, C. T. K., Cuc, P. T. The prolongation of central extensions. International Journal of Group Theory, 2012; 1(2): 39-49. doi: 10.22108/ijgt.2012.740
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