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http://dx.doi.org/10.4134/BKMS.b150297

ON THE TOPOLOGY OF THE NONABELIAN TENSOR PRODUCT OF PROFINITE GROUPS  

Russo, Francesco G. (Department of Mathematics and Applied Mathematics University of Cape Town)
Publication Information
Bulletin of the Korean Mathematical Society / v.53, no.3, 2016 , pp. 751-763 More about this Journal
Abstract
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.
Keywords
pro-p-groups; nonabelian exterior square; homology; topological groups; profinite groups;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 R. Brown, P. Higgins, and R. Sivera, Nonabelian algebraic topology, Filtered spaces, crossed complexes, cubical homotopy groupoids, EMS Tracts in Mathematics 15, Zurich, 2011.
2 R. Brown, D. L. Johnson, and E. F. Robertson, Some computations of non-abelian tensor products of groups, J. Algebra 111 (1987), no. 1, 177-202.   DOI
3 R. Brown and J.-L. Loday, Van Kampen theorems for diagrams of spaces, Topology 26 (1987), no. 3, 311-335.   DOI
4 B. Eick, Schur multiplicators of infinite pro-p-groups with finite coclass, Israel J. Math. 166 (2008), 147-156.   DOI
5 M. I. Graev, Free topological groups, Izv. Akad. Nauk SSSR Ser. Mat. 12 (1948), 279-324.
6 K. H. Hofmann and S. A. Morris, The Structure of Compact Groups, de Gruyter, Berlin, 2006.
7 N. Inassaridze, Nonabelian tensor products and nonabelian homology of groups, J. Pure Appl. Algebra 112 (1996), no. 2, 191-205.   DOI
8 E. Katz and S. A. Morris, Free products of topological groups with amalgamation I, Pacific J. Math. 119 (1985), no. 1, 169-180.   DOI
9 E. Katz and S. A. Morris, Free products of topological groups with amalgamation II, Pacific J. Math. 120 (1985), no. 1, 123-130.   DOI
10 M. S. Khan and S. A. Morris, Free products of topological groups with central amalgamation I, Trans. Amer. Math. Soc. 273 (1982), no. 2, 405-416.   DOI
11 M. S. Khan and S. A. Morris, Free products of topological groups with central amalgamation II, Trans. Amer. Math. Soc. 273 (1982), no. 2, 417-432.   DOI
12 C. R. Leedham-Green and S. McKay, The Structure of Groups of Prime Power Order, Oxford University Press, Oxford, 2002.
13 A. Lubotzky and D. Segal, Subgroups Growth, Progress in Mathematics (Boston, Mass.) 212, Birkhuser, Basel, 2003.
14 P. Moravec, On the Schur multipliers of finite p-groups of given coclass, Israel J. Math. 185 (2011), 189-205.   DOI
15 P. Niroomand and F. G. Russo, A note on the exterior centralizer, Arch. Math. (Basel) 93 (2009), no. 6, 505-512.   DOI
16 P. Niroomand and F. G. Russo, On the size of the third homotopy group of the suspension of an EilenbergMacLane space, Turkish J. Math. 38 (2014), no. 4, 664-671.   DOI
17 D. E. Otera, F. G. Russo, and C. Tanasi, Some algebraic and topological properties of the nonabelian tensor product, Bull. Korean Math. Soc. 50 (2013), no. 4, 1069-1077.   DOI
18 R. Rezaei and F. G. Russo, Exterior degree of infinite groups, preprint, 2013, ArXiv, available online at: http://arxiv.org/abs/1303.2324.
19 J. Rotman, An Introduction to Algebraic Topology, Springer, Berlin, 1988.