Schur multipliers and the Lazard correspondence
- 260 Downloads
Let G be a finite p-group of nilpotency class less than p−1, and let L be the Lie ring corresponding to G via the Lazard correspondence. We show that the Schur multipliers of G and L are isomorphic as abelian groups and that every Schur cover of G is in Lazard correspondence with a Schur cover of L. Further, we show that the epicenters of G and L are isomorphic as abelian groups. Thus the group G is capable if and only if the Lie ring L is capable.
Mathematics Subject Classification (2000)17B30 20D15 20F18 20F40
KeywordsSchur multiplier p-groups Lie rings Lazard correspondence
Unable to display preview. Download preview PDF.
- 2.A. Bak et al. Homology of multiplicative Lie rings. J. Pure Appl. Algebra 208 (2007), 761–777.Google Scholar
- 4.Bourbaki N.: Groupes et algèbres de Lie, Chapitre II. Hermann, Paris (1972)Google Scholar
- 7.M. Horn and S. Zandi Computing Schur multipliers and epicenters of Lie rings. In preparation, 2012.Google Scholar
- 9.Robinson D.: A course in the theory of groups. 2nd edition. Springer, New York (1995)Google Scholar
- 11.C. A. Weibel Homological Algebra. Cambridge University Press, Cambridge 38, 1994.Google Scholar