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Proceedings of the London Mathematical Society Advance Access originally published online on October 25, 2007
Proceedings of the London Mathematical Society 2008 96(1):227-250; doi:10.1112/plms/pdm033
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© 2007 London Mathematical Society

Injectivity theorems and algebraic closures of groups with coefficients

Jae Choon Cha

Department of Mathematics
Pohang University of Science and Technology
Pohang, Kyungbuk 790–784
Republic of Korea

Received 19 April 2006. Revision received 27 February 2007.

Recently, Cochran and Harvey defined torsion-free derived series of groups and proved an injectivity theorem on the associated torsion-free quotients. We show that there is a universal construction which extends such an injectivity theorem to an isomorphism theorem. Our result relates injectivity theorems to a certain homology localization of groups. In order to give a concrete combinatorial description and existence proof of the necessary homology localization, we introduce a new version of algebraic closures of groups with coefficients by considering certain types of equations.

2000 Mathematics Subject Classification 20J05, 57M07, (primary), 55P60, 57M27, (secondary).


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