Hostname: page-component-7dd5485656-zklqj Total loading time: 0 Render date: 2025-10-31T12:33:54.305Z Has data issue: false hasContentIssue false
  • English
  • Français

THE NON-ABELIAN TENSOR PRODUCT OF FINITE GROUPS IS FINITE: A HOMOLOGY-FREE PROOF

Published online by Cambridge University Press:  25 August 2010

VIJI Z. THOMAS
VIJI Z. THOMAS*
Affiliation:
Department of Mathematical Sciences, State University of New York at Binghamton, Binghamton, NY 13902-6000, USA e-mail: vthomas@math.binghamton.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note, we give a homology-free proof that the non-abelian tensor product of two finite groups is finite. In addition, we provide an explicit proof that the non-abelian tensor product of two finite p-groups is a finite p-group.

Keywords

Primary 20F24Secondary 20J9920F99

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 3 , September 2010 , pp. 473 - 477
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

REFERENCES

1.Brown, R., Johnson, D. L. and Robertson, E. F., Some Computations of non-abelian tensor products of groups, J. Algebra 111 (1987), 177–202.CrossRefGoogle Scholar
2.Brown, R. and Loday, J. L., Excision homotopique en basse dimension, C.R. Acad. Sci. Ser. I Math. Paris 298 (1984), 353–356.Google Scholar
3.Brown, R. and Loday, J. L., Van Kampen theorems for diagrams of spaces, Topology 26 (1987), 311–335.CrossRefGoogle Scholar
4.Dietzmann, A. P., On p-groups, Dokl. Akad. Nank, SSSR 15 (1937), 71–76.Google Scholar
5.Ellis, G. J., The non-abelian tensor product of finite groups is finite, J. Algebra 111 (1987), 203–205.CrossRefGoogle Scholar
6.Ellis, G. J. and Leonard, F., Computing Schur multipliers and tensor products of finite groups, Proc. R. Irish Acad. Sect. A 95 (1995), 137–147.Google Scholar
7.Kappe, L.-C., Nonabelian tensor products of groups: The commutator connection, in Proceedings Groups – St. Andrews at Bath (Campbell, C. M., Robertson, E. F., Ruskuc, N. and Smith, G. C., Editors), London Mathematical Society Lecture Notes, No 261 (Cambridge University Press, Cambridge, UK, 1999), 447–454.Google Scholar
8.Nakaoka, I. N., Non-abelian tensor products of solvable groups, J. Group Theory 3 (2000), 157–167.CrossRefGoogle Scholar
9.Robinson, D. J. S., Finiteness conditions and generalized soluble groups, Part I (Springer-Verlag, New York, Heidelberg, Berlin, 1972).CrossRefGoogle Scholar
10.Visscher, M. P., On the nilpotency and solvability length of nonabelian tensor products of groups, Arch. Math. 73 (1999), 161–171.CrossRefGoogle Scholar