ON THE CLASSIFICATION OF GROUPS OF PRIME-POWER ORDER BY COCLASS: THE 3-GROUPS OF COCLASS 2-Reference-Cited by-同舟云学术

ON THE CLASSIFICATION OF GROUPS OF PRIME-POWER ORDER BY COCLASS: THE 3-GROUPS OF COCLASS 2

Published:2013-08 Issue:05 Volume:23 Page:1243-1288
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

EICK BETTINA¹,LEEDHAM-GREEN C. R.²,NEWMAN M. F.³,O'BRIEN E. A.⁴

Affiliation:

1. Institut Computational Mathematics, Universität Braunschweig, 38016 Braunschweig, Germany

2. School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK

3. Mathematical Sciences Institute, Australian National University, ACT 0200, Australia

4. Department of Mathematics, University of Auckland, Auckland, New Zealand

Abstract

In this paper we take a significant step forward in the classification of 3-groups of coclass 2. Several new phenomena arise. Theoretical and computational tools have been developed to deal with them. We identify and are able to classify an important subset of the 3-groups of coclass 2. With this classification and further extensive computations, it is possible to predict the full classification. On the basis of the work here and earlier work on the p-groups of coclass 1, we formulate another general coclass conjecture. It implies that, given a prime p and a positive integer r, a finite computation suffices to determine the p-groups of coclass r.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196713500252

Reference19 articles.

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2. On a special class of p-groups

3. Periodic patterns in the graph of p-groups of maximal class

4. A new pattern in the graph ofp-groups of maximal class

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