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
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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.

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Additional Information

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