Classifying 2-groups by coclass
Abstract: Now that the conjectures of Leedham-Green and Newman have been proved, we probe deeper into the classification of -groups using coclass. We determine the pro--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.
M. F. Newman
Affiliation: School of Mathematical Sciences, Australian National University, Canberra, ACT 0200, Australia
E. A. O'Brien
Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
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