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- W2950318503 abstract "A. K. Bousfield's $Hmathbb Z$-localization of groups inverts homologically two-connected homomorphisms of groups. J. P. Levine's algebraic closure of groups inverts homomorphisms between finitely generated and finitely presented groups which are homologically two-connected and for which the image normally generates. We resolve an old problem concerning Bousfield $Hmathbb Z$-localization of groups, and answer two questions of Levine regarding algebraic closure of groups. In particular, we show that the kernel of the natural homomorphism from a group $G$ to it's Bousfield $Hmathbb Z$-localization is not always a $G$-perfect subgroup. In the case of algebraic closure of groups, we prove the analogous result that this kernel is not always an invisible subgroup." @default.
- W2950318503 created "2019-06-27" @default.
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- W2950318503 date "2013-06-25" @default.
- W2950318503 modified "2023-09-27" @default.
- W2950318503 title "Group localization and two problems of Levine" @default.
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