Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Classifying 2-groups by coclass


Authors: M. F. Newman and E. A. O'Brien
Journal: Trans. Amer. Math. Soc. 351 (1999), 131-169
MSC (1991): Primary 20D15; Secondary 20-04
MathSciNet review: 1458332
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Now that the conjectures of Leedham-Green and Newman have been proved, we probe deeper into the classification of $p$-groups using coclass. We determine the pro-$2$-groups of coclass at most 3 and use these to classify the 2-groups of coclass at most 3 into families. Using extensive computational evidence, we make some detailed conjectures about the structure of these families. We also conjecture that the 2-groups of arbitrary fixed coclass exhibit similar behaviour.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 20D15, 20-04

Retrieve articles in all journals with MSC (1991): 20D15, 20-04


Additional Information

M. F. Newman
Affiliation: School of Mathematical Sciences, Australian National University, Canberra, ACT 0200, Australia
Email: newman@maths.anu.edu.au

E. A. O'Brien
Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
Email: obrien@math.auckland.ac.nz

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02124-8
PII: S 0002-9947(99)02124-8
Keywords: $p$-groups, pro-$p$-groups, coclass
Received by editor(s): November 1, 1996
Additional Notes: O’Brien was supported by the Alexander von Humboldt Foundation, Bonn, via a Research Fellowship held at the Lehrstuhl D für Mathematik, RWTH Aachen, and by a Visiting Fellowship at the School of Mathematical Sciences, Australian National University. We thank Rodney James, C.R. Leedham-Green, and W. Plesken for helpful discussions.
Article copyright: © Copyright 1999 American Mathematical Society