JOURNAL BROWSE
Search
Advanced SearchSearch Tips
ON THE TOPOLOGY OF THE NONABELIAN TENSOR PRODUCT OF PROFINITE GROUPS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
ON THE TOPOLOGY OF THE NONABELIAN TENSOR PRODUCT OF PROFINITE GROUPS
Russo, Francesco G.;
  PDF(new window)
 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;
 Language
English
 Cited by
1.
Strong subgroup commutativity degree and some recent problems on the commuting probabilities of elements and subgroups, Quaestiones Mathematicae, 2016, 39, 8, 1019  crossref(new windwow)
2.
The Influence of the Complete Nonexterior Square Graph on some Infinite Groups, Lithuanian Mathematical Journal, 2016, 56, 4, 492  crossref(new windwow)
 References
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. crossref(new window)

3.
R. Brown and J.-L. Loday, Van Kampen theorems for diagrams of spaces, Topology 26 (1987), no. 3, 311-335. crossref(new window)

4.
B. Eick, Schur multiplicators of infinite pro-p-groups with finite coclass, Israel J. Math. 166 (2008), 147-156. crossref(new window)

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. crossref(new window)

8.
E. Katz and S. A. Morris, Free products of topological groups with amalgamation I, Pacific J. Math. 119 (1985), no. 1, 169-180. crossref(new window)

9.
E. Katz and S. A. Morris, Free products of topological groups with amalgamation II, Pacific J. Math. 120 (1985), no. 1, 123-130. crossref(new window)

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. crossref(new window)

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. crossref(new window)

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. crossref(new window)

15.
P. Niroomand and F. G. Russo, A note on the exterior centralizer, Arch. Math. (Basel) 93 (2009), no. 6, 505-512. crossref(new window)

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. crossref(new window)

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. crossref(new window)

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.