Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-18T01:43:03.932Z Has data issue: false hasContentIssue false
  • English
  • Français

Second Fox Subgroups of Arbitrary Groups

Published online by Cambridge University Press:  20 November 2018

Mario Curzio  and
C. Kanta Gupta
Mario Curzio
Affiliation:
Department of Mathematics, University of Napolivia Cinitia, Napoli 80126, Italy
C. Kanta Gupta
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2
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.

We give a complete description of the second Fox subgroup G ∩ (1 + Δ2(G)Δ(H)) relative to a given normal subgroup H of an arbitrary finitely generated group G.

Keywords

20C0716A27
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 2 , 01 June 1995 , pp. 177 - 181
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Bergman, G. M. and Dicks, W., On universal derivations, J. Algebra 36( 1975), 193—211.Google Scholar
2. Enright, D. E., Triangular matrices over group rings, Doctoral Thesis, New York University, 1968.Google Scholar
3. Gruenberg, K. W., Cohomological Topics in Group Theory, Lecture Notes in Math. 143, Springer-Verlag, 1970.Google Scholar
4. Gupta, C. K., Subgroups of free groups induced by certain products of augmentation ideals, Comm. Algebra 6(1978), 1231–1238.Google Scholar
5. Gupta, C. K. and Gupta, N. D., Power series and matrix representations of certain relatively free groups, Proc. Second Internat. Conf. Theory of Groups, Canberra, 1973, In: Lecture Notes in Math. 372, Springer- Verlag, 1974,318–329.Google Scholar
6. Gupta, N., Fox subgroups of free groups, J. Pure Appl. Algebra 11(1977), 1—17.Google Scholar
7. Gupta, N., Fox subgroups of free groups II, Contemp. Math. 33(1984), 223—231.Google Scholar
8. Gupta, N., Free Groups Rings, Contemp. Math. Amer. Math. Soc. 66(1987).Google Scholar
9. Hurley, T. C., On a problem of Fox, Invent. Math. 21(1973), 294–299.Google Scholar
10. Hurley, T. C., Identifications in a free group, J. Pure Appl. Algebra 48(1987), 249–261.Google Scholar
11. Khambadkone, M., On the structure of augmentation ideals in group rings, J. Pure Appl.Algebra 35( 1985), 35–45.Google Scholar
12. Magnus, W., Karrass, A. and Solitar, D., Combinatorial Group Theory, Interscience, New York, 1966.Google Scholar
13. Yunus, I. A., On a problem of Fox, Soviet Math. Dokl. 30(1984), 346–350.Google Scholar