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The properties of the nonabelian tensor products are interesting in different contexts of algebraic topology and group theory. We prove two theorems, dealing with the nonabelian tensor products of projective limits of finite groups. The first describes their topology. Then we show a result of embedding in the second homology group of a pro-$p$-group, via the notion of complete exterior centralizer. We end with some open questions, originating from these two results.
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참고문헌 (19)
참고문헌 신청
R. Brown / 2011 / Nonabelian algebraic topology, Filtered spaces, crossed complexes, cubical homotopy groupoids / EMS Tracts in Mathematics 15
R. Brown / 1987 / Some computations of non–abelian tensor products of groups / J. Algebra 111(1):177~202
R. Brown / 1987 / Van Kampen theorems for diagrams of spaces / Topology 26(3):311~335
B. Eick / 2008 / Schur multiplicators of infinite pro–p–groups with finite coclass / Israel J. Math 166:147~156
M. I. Graev / 1948 / Free topological groups / Izv. Akad. Nauk SSSR Ser. Mat 12:279~324
R. Brown / 1987 / Some computations of non–abelian tensor products of groups / J. Algebra 111(1):177~202
R. Brown / 1987 / Van Kampen theorems for diagrams of spaces / Topology 26(3):311~335
B. Eick / 2008 / Schur multiplicators of infinite pro–p–groups with finite coclass / Israel J. Math 166:147~156
M. I. Graev / 1948 / Free topological groups / Izv. Akad. Nauk SSSR Ser. Mat 12:279~324
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