On T-systems of groups

M. J. Dunwoody

doi:10.1017/S1446788700027919

Extract

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.

Let G be an n-generator group and let g = (g1, g2, …, gn) be an ordered set of n elements which generate G, then g is called a generating n-vector of G. Let denote the set of all generating n-vectors of G.

References

[1]Neumann, Bernhard H. und Neumann, Hanna, Zwei Klassen charakteristischer Untergruppen und ihre Faktorgruppen. Math Nachr. 4 (1951) 106–125.Google Scholar

[2]Neumann, B. H., on a Question of Gaschütz. Archiv der Mathematik 7 (1956) 87–90.CrossRef Google Scholar

[3]Chevalley, Clude, Fundamental Concepts of Algebra. Academic press Inc., New York (1956).Google Scholar

[4]Gaschütz, Wolfgang, Zu einem von B. H. und H. Neumann gestelten Problem, Math Nachr. 14 (1955—1956) 249–252.Google Scholar

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Dyer, Joan Landman 1969. On the isomorphism problem for polycyclic groups. Mathematische Zeitschrift, Vol. 112, Issue. 2, p. 145.

Dunwoody, M. J. and Pietrowski, A. 1973. Presentations of the Trefoil Group. Canadian Mathematical Bulletin, Vol. 16, Issue. 4, p. 517.

Pride, Stephen J. 1975. On the generation of one-relator groups. Transactions of the American Mathematical Society, Vol. 210, Issue. 0, p. 331.

Brunner, Andrew Michael 1978. Metabelian representations and the isomorphism problem. Mathematische Zeitschrift, Vol. 162, Issue. 3, p. 235.

Evans, Martin J. 1993. T-systems of certain finite simple groups. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 113, Issue. 1, p. 9.

Lubotzky, Alexander and Pak, Igor 2000. The product replacement algorithm and Kazhdan’s property (T). Journal of the American Mathematical Society, Vol. 14, Issue. 2, p. 347.

Lubotzky, Alexander 2001. Pro-finite Presentations. Journal of Algebra, Vol. 242, Issue. 2, p. 672.

McCullough, Darryl and Wanderley, Marcus 2003. Free actions on handlebodies. Journal of Pure and Applied Algebra, Vol. 181, Issue. 1, p. 85.

Avni, Nir and Garion, Shelly 2008. Connectivity of the Product Replacement Graph of simple groups of bounded Lie rank. Journal of Algebra, Vol. 320, Issue. 2, p. 945.

Garion, Shelly 2008. Connectivity of the product replacement algorithm graph of PSL(2, q). Journal of Group Theory, Vol. 11, Issue. 6,

Garion, Shelly and Shalev, Aner 2009. Commutator maps, measure preservation, and 𝑇-systems. Transactions of the American Mathematical Society, Vol. 361, Issue. 9, p. 4631.

Crestani, Eleonora and Lucchini, Andrea 2013. The graph of the generating d-tuples of a finite soluble group and the swap conjecture. Journal of Algebra, Vol. 376, Issue. , p. 79.

MCCULLOUGH, DARRYL and WANDERLEY, MARCUS 2013. NIELSEN EQUIVALENCE OF GENERATING PAIRS OF SL(2,q). Glasgow Mathematical Journal, Vol. 55, Issue. 3, p. 481.

McCullough, Darryl 2014. Generating pairs and group actions. Journal of Pure and Applied Algebra, Vol. 218, Issue. 5, p. 777.

Jones, Gareth A. and Wolfart, Jürgen 2016. Dessins d'Enfants on Riemann Surfaces. p. 179.

Myropolska, Aglaia 2017. Nielsen equivalence in Gupta-Sidki groups. Proceedings of the American Mathematical Society, Vol. 145, Issue. 8, p. 3331.

Guyot, Luc 2017. On finitely generated modules over quasi-Euclidean rings. Archiv der Mathematik, Vol. 108, Issue. 4, p. 357.

Virchow, Stefan-C. 2019. Application of character estimates to the number of 𝑇2-systems of the alternating group. Journal of Group Theory, Vol. 22, Issue. 5, p. 845.

Article contents

On T-systems of groups

Extract

References

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests