On the classification of groups of prime-power order by coclass: The 3-groups of coclass 2

Bettina Eick, C. R. Leedham-Green, M. F. Newman, E. A. O'Brien

    Research output: Contribution to journalArticlepeer-review

    10 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)1243-1288
    Number of pages46
    JournalInternational Journal of Algebra and Computation
    Volume23
    Issue number5
    DOIs
    Publication statusPublished - Aug 2013

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