Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-22T02:16:27.304Z Has data issue: false hasContentIssue false
  • English
  • Français

THE LOWER RANK OF DIRECT PRODUCTS OF HEREDITARILY JUST INFINITE GROUPS

Part of: Special aspects of infinite or finite groups Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  04 September 2017

BENJAMIN KLOPSCH  and
MATTEO VANNACCI
BENJAMIN KLOPSCH
Affiliation:
Mathematisches Institut der Heinrich-Heine-Universität, Universitätsstr. 1, 40225 Düsseldorf, Germany e-mails: [email protected], [email protected]
MATTEO VANNACCI
Affiliation:
Mathematisches Institut der Heinrich-Heine-Universität, Universitätsstr. 1, 40225 Düsseldorf, Germany e-mails: [email protected], [email protected]
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 determine the lower rank of the direct product of finitely many hereditarily just infinite profinite groups of finite lower rank.

MSC classification

Primary: 20E18: Limits, profinite groups
Secondary: 20F06: Cancellation theory; application of van Kampen diagrams
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 1 , January 2018 , pp. 225 - 230
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

REFERENCES

1. Barnea, Y., Generators of simple Lie algebras and the lower rank of some pro-p-groups, Comm. Algebra 30 (3) (2002), 1293–1303.CrossRefGoogle Scholar
2. Dixon, J. D., du Sautoy, M. P. F., Mann, A. and Segal, D., Analytic pro-p groups, Cambridge Studies in Advanced Mathematics, vol. 61 (Cambridge University Press, Cambridge, 1999).CrossRefGoogle Scholar
3. Ershov, M. and Jaikin-Zapirain, A., Groups of positive weighted deficiency and their applications, J. Reine Angew. Math. 677 (2013), 71–134.Google Scholar
4. Klaas, G., Leedham-Green, C. R. and Plesken, W., Linear pro-p-groups of finite width, Lecture Notes in Mathematics, vol. 1674 (Springer-Verlag, Berlin, 1997).CrossRefGoogle Scholar
5. Kuranishi, M., On everywhere dense imbedding of free groups in Lie groups, Nagoya Math. J. 2 (1951), 63–71.CrossRefGoogle Scholar
6. Lazard, M., Groupes analytiques p-adiques, Inst. Hautes Études Sci. Publ. Math. 26 (1965), 389–603.Google Scholar
7. Lubotzky, A. and Mann, A., Powerful p-groups. II. p-adic analytic groups, J. Algebra 105 (2) (1987), 506–515.CrossRefGoogle Scholar
8. Lubotzky, A. and Shalev, A., On some Λ-analytic pro-p groups, Israel J. Math. 85 (1–3) (1994), 307–337.CrossRefGoogle Scholar
9. Reid, C. D., On the structure of just infinite profinite groups, J. Algebra 324 (9) (2010), 2249–2261.CrossRefGoogle Scholar
10. Vannacci, M., On hereditarily just infinite profinite groups obtained via iterated wreath products, J. Group Theory 19 (2) (2016), 233–238.Google Scholar